acer

23090 Reputation

29 Badges

15 years, 307 days

Social Networks and Content at Maplesoft.com

"My friend George Mallory… once did an inexplicable climb on Snowdon. He had left his pipe on a ledge, half-way down one of the Liwedd precipices, and scrambled back by a short cut to retrieve it, then up again by the same route. No one saw what route he took, but when they came to examine it the next day for official record, they found an overhang nearly all the way. By a rule of the Climbers' Club, climbs are never named in honour of their inventors, but only describe natural features. An exception was made here. The climb was recorded as follows: 'Mallory's Pipe, a variation on route 2; see adjoining map. This climb is totally impossible. It has been performed once, in failing light, by Mr G. H. L. Mallory.'." -- "Goodbye to All That", Robert Graves

MaplePrimes Activity


These are replies submitted by acer

Could you attach a text file of the actual (irregular) data? That'd help.

[edit: I've been able to grind out a nice, smooth plot of m__zz vs m__yy and n, using explicit piecewise derived from your formula. I'll try to find time to post later. This may help (as well as look smoother).]

@tomleslie The SolveEquations command in the DirectSearch package (ver. 1 or 2) has a serious flaw, and I do not recommend it be used for numeric rootfinding unless special care is taken.

Specifically, it can disregard its own error-tolerance option, thereby indicating that a root has been found which satisfies the equations to within the tolerance requested, when in fact no such value has been attained (or even exists).

One reasonable amendment is to wrap SolveEquations in a procedure which computes the forward errors on its own, and indicates in the case that the purported solution is not within the requested accuracy.

@Angelo Melino I always try the so-called operator form calling sequence of evalf(Int(...)) when trying to handle difficulties. By that I mean that the integrand is supplied as an operator or procedure. In part I do so because it's one way to forcibly skip the (sometimes very expensive) symbolic continuity check of the integrand.

For your example that showed me that evalhf was balking on the LegendreP call.

The precise error message coming out of evalhf was unfamiliar to me, which is somewhat unusual. Now, some commands that have both fast evalhf modes and slower/fallback evalf mode will try...catch the former. Some of these commands are coded to do the fallback only if the error is an, ummm, "non-evalhf'ability error", where the code is manifestly non-evalhf'able. If another kind of deeper problem occurs with the call then there may be little merit in falling back to evalf; that is a rationale, for good or bad. But this approach is not robust unless it can be coded to catch all the sorts of error that typically arise when trying to evalhf a call that is non-evalhf'able (given that earlier code ensures that the call is otherwise correct up to a point).

Another approach is to fall back to evalf upon any error encountered during an earlier evalhf attempt.

I have seen both kinds of approach:  the blanket fallback and the fallback only on certain caught errors.  Eg, in plotting, Optimization, evalf(Int(...)), etc.

Since the error message I saw here was unfamiliar to me, it occurred to me that it might just be the case that the fallback was not being tried, perhaps just because the mechanism was not coded to catch this particular error message from evalhf. So I forced another kind of evalhf error.

I have not taken the time yet to run it all in the debugger and see whether my suppositions are correct about this example.

restart

istar := y*sinh(Pi*y)*exp(-alpha*y^2)*LegendreP(-1/2+I*y, 1+u)

alpha := 1; u := 2

Hre_oops := unapply(Re(istar), y)

proc (y) options operator, arrow; Re(y*sinh(Pi*y)*exp(-y^2)*LegendreP(-1/2+I*y, 3)) end proc

evalf(Int(Hre_oops, 0 .. infinity, method = _d01amc))

Error, (in evalf/int) evalhf cannot use _passed or args

foo := eval(istar, y = 1)

sinh(Pi)*exp(-1)*LegendreP(-1/2+I, 3)

evalhf(foo)

Error, evalhf cannot use _passed or args

evalf(foo)

1.340415046+0.*I

evalhf(LegendreP(-1/2+I, 3))

Error, evalhf cannot use _passed or args

evalf(LegendreP(-1/2+I, 3))

.3154998782+0.*I

evalhf(Hre_oops(1))

Error, evalhf cannot use _passed or args

evalf(Hre_oops(1))

1.340415046+0.*I

Hre := proc (Y) []; eval(Re(istar), y = Y) end proc

evalhf(Hre(1))

Error, unable to evaluate expression to hardware floats: []

``

Download Istar_ac_ac.mw

It can get ricky, to provide fast evalhf mode alongside an evalf fallback. Other subtleties include detecting and passing back errors in the user's whole formulation, ascertaining which errors to re-throw and which to subsume, etc.

Automatic fallback mechanisms are nice for users, but also harder to maintain. One danger is that an upstream method can be accidentally broken while that fact is obscured by the very robustness of the mechanism.

@maple_user_2017 I have added an additional answer below, showing a few ways in which explicit, exact roots may be obtained for your system.

@tomleslie Your guess about what's going on is mistaken. The essence of what makes your code work is not that the input of the system is as a list.

Your code works because of the order in which your choice of list happens to force the equations to be processed. If you reverse the order of the equations in the list then once again fsolve will return unevaluated here (which you mention in your point "3").

The lexicographic set order of these equations happens to match the list order of these equations which also fails.

But your claim that the problem is due to how fsolve prefers or deals with lists versus sets per se is wrong. This sentence you wrote is simply untrue, "the fsolve() command doesn't like solving sets of equations - it much prefers lists."

restart:
kernelopts(version);

`Maple 2016.2, X86 64 LINUX, Jan 13 2017, Build ID 1194701`

S:=t->c*exp(-a*t)+18:

sys1:={S(2)=55,S(8)=36};
fsolve(sys1);

{c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}

fsolve({c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}, {a, c})

sys2:=[S(2)=55,S(8)=36];
fsolve(sys2);

[c*exp(-2*a)+18 = 55, c*exp(-8*a)+18 = 36]

{a = .1200910258, c = 47.04478236}

sys3:=[S(8)=36,S(2)=55];
fsolve(sys3);

[c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55]

fsolve([c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55], {a, c})

 

Download list_rev.mw

This is similar to what I'd previously alluded: a lexicographic ordering may happen to bystep the coding flaw that prevents further initial points from being tried. Your use of one successful list input is another way to force such a fortuitous bypass. But it's the particular order that makes the difference, not the fact that the input is a list. A list in the reverse order also fails.

@Carl Love I think that your supposition about the principal cause of failure is not correct for this particular example.

What's happening for this example (in Maple 2016.2 at least) is that the iterative approach is not converging (even close to any root) for the very first chosen initial point. And then (strangely, and as the principal problem here) it is returning as failed and trying no additional initial points.

It ought to be trying additional initial points. That's what it does when I simply switch the variable names (ie. a->C and c->A) with the new names being in the opposite alphabetical order.

I have yet not pinpointed the problem in the code and a good (reliable) fix. But I will definitely be submitting this as a bug report.

@Rouben Rostamian  

1) The visible edges of the rendered 3d surface are not anti-aliased. That is clearly visible for a variety of simple 3D plots. I have previously inquired about this, and was recently told that enabling some related options in the graphics renderer (JOGL?) might produce some undesirable effects alongside anti-aliasing.

2) The OP already noted that he'd experimented with the projection option, and found it wanting (esp, wrt lighting drop-off as a function of projection effect).

3) A custom light source is already possible, using options.

4) Multiple light sources are not currently possible, that's true. I have previously submitted requests about this (SCR=Software Change Request), as have certain other people.

@emendes Try using,

  IntegrationTools:-Parts

It's pretty straightforward, here.

Is your objection a solution (depending on the particular example) for which some of the individual log calls evaluate to a nonreal value?

You have not explained your issue clearly.

Someone defaced this page and its title.

Originally is was titled,

"Modular Square Root of a number (mod n), knowing factorization of n"

And its contents were,

"ModularSquareRoot can't handle a really big n because of the factorization problem. But I would like to know if there is any other function than can use as parameters the factorization of n.

I already have an algorithm that does that for n=pq with p, q primers, and could generalize it, but I was wondering whether there was a built-in function that does that."

@Teep I would agree with Tom that it's more straightforward to specify the grid size in terms of the number of blocks horizontally and vertically (rather than as a refinement ratio).

Here is a more general example (uglier end-points, without just an integer range).

It uses seq in a similar manner than I had above, but adjusted for this way of specifying the numbers of blocks.

The procedure C can compute the position of an inner block.
 

restart

with(plots)

x_min := -1.2; x_max := 4.3; y_min := -2.3; y_max := 3.8

-1.2

4.3

-2.3

3.8

x_range := x_max-x_min; y_range := y_max-y_min

5.5

6.1

nx[0] := 3; ny[0] := 2

3

2

Blocks := nx[0]*ny[0]

6

Points1 := [seq(seq([X, Y], X = x_min .. x_max, x_range/nx[0]), Y = y_min .. y_max, y_range/ny[0])]; nops(%); (nx[0]+1)*(ny[0]+1)

[[-1.2, -2.3], [.633333333, -2.3], [2.466666666, -2.3], [4.299999999, -2.3], [-1.2, .750000000], [.633333333, .750000000], [2.466666666, .750000000], [4.299999999, .750000000], [-1.2, 3.800000000], [.633333333, 3.800000000], [2.466666666, 3.800000000], [4.299999999, 3.800000000]]

12

12

plot(Points1, style = point, color = red, symbol = solidcircle, symbolsize = 20)

nx[1] := 3*3; ny[1] := 3*2

9

6

Blocks := nx[1]*ny[1]

54

Points2 := [seq(seq([X, Y], X = x_min .. x_max, x_range/nx[1]), Y = y_min .. y_max, y_range/ny[1])]; nops(%); (nx[1]+1)*(ny[1]+1)

60

70

P1 := pointplot(Points2, color = red, symbol = solidcircle, symbolsize = 15); P1

Typesetting:-mrow(Typesetting:-mi("C", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo("proc", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("xidx", italic = "true", mathvariant = "italic"), Typesetting:-mo("∷", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("posint", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("yidx", italic = "true", mathvariant = "italic"), Typesetting:-mo("∷", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("posint", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("nx", italic = "true", mathvariant = "italic"), Typesetting:-mo("∷", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("posint", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("ny", italic = "true", mathvariant = "italic"), Typesetting:-mo("∷", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("posint", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mi(""), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("xidx", italic = "true", mathvariant = "italic"), Typesetting:-mo(">", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("nx", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("then", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("error", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-ms("xidx cannot be greater than nx, %1, but received %2"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("nx", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("xidx", italic = "true", mathvariant = "italic"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("yidx", italic = "true", mathvariant = "italic"), Typesetting:-mo(">", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("ny", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("then", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("error", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-ms("yidx cannot be greater than ny, %1, but received %2"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("ny", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("yidx", italic = "true", mathvariant = "italic"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x_min", italic = "true", mathvariant = "italic"), Typesetting:-mo("+", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mfrac(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("xidx", italic = "true", mathvariant = "italic"), Typesetting:-mo("&uminus0;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mfrac(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("2", mathvariant = "normal")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false")), mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("nx", italic = "true", mathvariant = "italic")), mathvariant = "normal")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("⋅", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x_max", italic = "true", mathvariant = "italic"), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x_min", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("y_min", italic = "true", mathvariant = "italic"), Typesetting:-mo("+", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mfrac(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("yidx", italic = "true", mathvariant = "italic"), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mfrac(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("2", mathvariant = "normal")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false")), mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ny", italic = "true", mathvariant = "italic")), mathvariant = "normal")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("⋅", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y_max", italic = "true", mathvariant = "italic"), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("y_min", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("proc", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"))

C(9, 1, nx[1], ny[1])

[3.994444444, -1.791666667]

display(P1, pointplot(C(9, 1, nx[1], ny[1]), color = blue, symbol = solidcircle, symbolsize = 20), pointplot([C(4, 5, nx[1], ny[1]), C(3, 2, nx[1], ny[1])], color = blue, symbol = solidcircle, symbolsize = 20))

 

``

Download Grid_Example_ac2.mw

@MapleUser2017 The name of the module is MyMat.

So you'd load it using the  with(MyMat)  call.

You keep trying to utilize the name MyLib to refer to the module which you had assigned to MyMat, but that's wrong. The name MyLib is just a name that you introduced for referring to the .mla filename or its location.

This has been mentioned about 4 or 5 times now. It seems that the problem lies not in your Maple installation.

Upload an attachment that contain a definition for f(x,y).

It need not recreate f by previous computations (integrations or what have you). You may be able to lprint the call f(x,y).

But being able to reproduce the issue is important.

Long explanations alone are less useful, for a performance issue.

Could you upload an attachment which can be used to recreate the precise issue?

It only need contain the definition of f(x,y), not all the lead-up computations (integrations, say) to it.

You might be able to just lprint the result of the call f(x,y).

@Adam Ledger My point was not about the fact that `^` is a kernel builtin. My point was that there's no reason to think that the implementation would be the most naive full iterated multiplication.

For big integers it might call a GMP function, so perhaps see here. But why wouldn't all integers be handled as well as that.

I don't understand what you mean by "which factorization". The exponent is stored in binary.

First 73 74 75 76 77 78 79 Last Page 75 of 464