vv

9132 Reputation

18 Badges

5 years, 237 days

MaplePrimes Activity


These are questions asked by vv

Is it possible to split an execution group containing 2D input?
(without conversion to 1D which destroys the format).
Using F3 or the menu seems to work only for lines with a prompt.
But usually an execution group has a single prompt; lines with prompts appear e.g. when two execution groups are joined (with F4).
Is copy&paste the only solution?

Strange (inconsistent) behavior of eval in piecewise

 

restart;#####################

a:=2:

p:=piecewise(x<a, 1/(x-a), x=a, 22, 33);

p := piecewise(x < 2, 1/(-2+x), x = 2, 22, 33)

(1)

eval(p, x=a);

22

(2)

restart;#####################

a:=Pi:

p:=piecewise(x<a, 1/(x-a), x=a, 22, 33);

p := piecewise(x < Pi, 1/(-Pi+x), x = Pi, 22, 33)

(3)

eval(p, x=a);

Error, (in eval/piecewise) numeric exception: division by zero

 

restart;#####################

a:=Pi+ln(2):

p:=piecewise(x<a, 1/(x-a), x=a, 22, 33);

p := piecewise(x < Pi+ln(2), 1/(-Pi-ln(2)+x), x = Pi+ln(2), 22, 33)

(4)

eval(p, x=a);

22

(5)

restart;#####################

a:=Pi+1:

p:=piecewise(x<a, 1/(x-a), x=a, 22, 33);

p := piecewise(x < Pi+1, 1/(-Pi-1+x), x = Pi+1, 22, 33)

(6)

eval(p, x=a);

Error, (in eval/piecewise) numeric exception: division by zero

 

restart;#####################

a:=gamma:

p:=piecewise(x<a, 1/(x-a), x=a, 22, 33);

p := piecewise(x < gamma, 1/(-gamma+x), x = gamma, 22, 33)

(7)

eval(p, x=a);

Error, (in eval/piecewise) numeric exception: division by zero

 

#######################

f:=x->piecewise(x<Pi, 1/(x-Pi), x=Pi, 22, 33);

f := proc (x) options operator, arrow; piecewise(x < Pi, 1/(x-Pi), x = Pi, 22, 33) end proc

(8)

f(Pi);

22

(9)

 


Download piecewise-strange.mw

Some of these seem to be difficult to explain ...

 

restart;

Digits:=3;

3

(1)

u:=1.23456;

1.23456

(2)

A := [1.23456, 1.23456+0, 1.23456+x+0, 1.23456+(x+0)];
B := [u,       u+0,       u+x+0,       u+(x+0)];

[1.23456, 1.23, 1.23+x, 1.23456+x]

 

[1.23456, 1.23456, 1.23456+x, 1.23456+x]

(3)

lprint(A); lprint(B);

[1.23456, 1.23, 1.23+x, 1.23456+x]

[1.23456, 1.23456, 1.23456+x, 1.23456+x]

 

is(A[1]=A[2]),    is(A[3]=A[4]);

true, true

(4)

evalb(A[1]=A[2]), evalb(A[3]=A[4]);

true, false

(5)

is(A=B);
is~(A=~B);

false

 

[true, true, true, true]

(6)

evalb(A=B);
evalb~(A=~B);

false

 

[true, true, false, true]

(7)

 

Download Difficult-to-explain.mw

restart;

f:=5*x^3-5*x+1;

5*x^3-5*x+1

(1)

s:=[solve(f)]; evalf(%);  # All the roots are real

[(1/30)*(-2700+(300*I)*219^(1/2))^(1/3)+10/(-2700+(300*I)*219^(1/2))^(1/3), -(1/60)*(-2700+(300*I)*219^(1/2))^(1/3)-5/(-2700+(300*I)*219^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/30)*(-2700+(300*I)*219^(1/2))^(1/3)-10/(-2700+(300*I)*219^(1/2))^(1/3)), -(1/60)*(-2700+(300*I)*219^(1/2))^(1/3)-5/(-2700+(300*I)*219^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/30)*(-2700+(300*I)*219^(1/2))^(1/3)-10/(-2700+(300*I)*219^(1/2))^(1/3))]

 

[.8788850663-0.2e-9*I, -1.088033915-0.2598076212e-9*I, .2091488484+0.2598076212e-9*I]

(2)

max(s);  # ?

Error, (in simpl/max) complex argument to max/min: (1/30)*(-2700+(300*I)*219^(1/2))^(1/3)+10/(-2700+(300*I)*219^(1/2))^(1/3)

 

type(s,list(realcons)); # Wrong, the type realcons should not be purely syntactic; or is it?

false

(3)

R:=convert(s,RootOf):

max(R);  #  For nested RootOfs fails

Error, (in simpl/max) complex argument to max/min: (1/30)*RootOf(_Z^3+2700-300*RootOf(_Z^2+1, index = 1)*RootOf(_Z^2-73, index = 1)*RootOf(_Z^2-3, index = 1), index = 1)+10/RootOf(_Z^3+2700-300*RootOf(_Z^2+1, index = 1)*RootOf(_Z^2-73, index = 1)*RootOf(_Z^2-3, index = 1), index = 1)

 

sort(s): evalf(%);  # Wrong

[.8788850663-0.2e-9*I, .2091488484+0.2598076212e-9*I, -1.088033915-0.2598076212e-9*I]

(4)

 

Workaround

 

S:=[seq(RootOf(f,x,index=i),i=1..3)];

[RootOf(5*_Z^3-5*_Z+1, index = 1), RootOf(5*_Z^3-5*_Z+1, index = 2), RootOf(5*_Z^3-5*_Z+1, index = 3)]

(5)

evalf(S);

[.2091488484, .8788850662, -1.088033915]

(6)

min(S);max(S);  # OK

RootOf(5*_Z^3-5*_Z+1, index = 3)

 

RootOf(5*_Z^3-5*_Z+1, index = 2)

(7)

sort(S);   # Wrong!

[RootOf(5*_Z^3-5*_Z+1, index = 1), RootOf(5*_Z^3-5*_Z+1, index = 2), RootOf(5*_Z^3-5*_Z+1, index = 3)]

(8)

################################

r:=(sqrt(2)+I)^3 + (sqrt(2)-I)^3;

(2^(1/2)+I)^3+(2^(1/2)-I)^3

(9)

type(r,realcons);  # Purely syntactic?

false

(10)

type(expand(r),realcons);

true

(11)

max(r,13);  # Even for such a simple expression?

Error, (in simpl/max) complex argument to max/min: (2^(1/2)+I)^3+(2^(1/2)-I)^3

 

 


Download TryHarder.mw

Here are two inocent Vectors.

V1 := Vector[row]([`+`, 1, 2]);

_rtable[18446744074366295326]

(1)

V2 := Vector[row]([1, `+`, 2]);

_rtable[18446744074366288110]

(2)

lprint(V1);

Vector[row](3, {1 = `+`, 2 = 1, 3 = 2}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

 

 

The questions:

 

1.  Try to guess the Maple's answer for:

 

V1, V2;

 

2. Try to explain.

 


Download v1v2.mw

4 5 6 7 8 9 10 Page 6 of 11