How about this equation

restart:
solve(x^2 - 2*(m+1)*x+m^2 - 2*m + m^2=0,{x},parametric=full);
allvalues(%);?

Greetings to all!

Recently I encouter the following issue:

Maple (version 17) coudn't recognize that 20.0 equals with 20 and with 20.00. Believe me, this is very annoying!

Do I miss something? Is there any command that do the trick?

Thank you!

Giorgos K.

Hi,

   I have a set of linear equations in terms of Ax+B=0, where A and B are matrices.

  I used linsolve or LinearSolve to solve the equations.

   Is there any simple way to run linsolve/LinearSolve parallelly? suppose I already have matrices A and B.

Thank you very much

#page 320 and 322 of book Singular introduction to commutative algebra

it return too many recursion 

hilbertseries([a+a*c, a+a*b, a+b+c]);

eq1 := a+a*c;

eq2 := a+a*b;

eq3 := a+b+c;

eq1a := Homogenize(eq1, h);

eq2a := Homogenize(eq2, h);

eq3a := Homogenize(eq3, h);

T3:=lexdeg([a,b,c,h]);

GB := Basis([eq1a,eq2a,eq3a], T3); #a

#MonomialHilbertPoincare(LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3));

with(PolynomialIdeals):

MonomialHilbertPoincare := proc (I3)

#I3:=[LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3)];

T2:=lexdeg([h,c,b,a]);

varj := [h,c,b,a];

I2 := InterReduce(I3, T2);

s := nops(I2);

if I2[1] = 0 then return 1 end if:

if I2[1] = 1 then return 0 end if:

if degree(I2[s]) = 1 then return (1-varj[1])^s end if:

lt := LeadingTerm(I2[s],T2);

leadexp := [degree(lt[2],h),degree(lt[2],c),degree(lt[2],b),degree(lt[2],a)];

j := 1;

for z from 1 to nops(leadexp) do

                if leadexp[j] = 0 then

                                j := j + 1;

                end if:

od:

finallist := [];

for z from 1 to nops(GB) do

                finallist := [op(finallist), GB[z]+varj[j]];

od:

quotientlist := Generators(Quotient(GB, varj[j]));

finallist2 := [];

for z from 1 to nops(quotientlist) do

                finallist2 := [op(finallist2), op(z,quotientlist)];

od:

return MonomialHilbertPoincare(finallist) + varj[1]*MonomialHilbertPoincare(finallist2);

end proc;

F:=[LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3)];

MonomialHilbertPoincare(F);

but if restart the program，the menu of Plot Builder is appear，in same function（x^2+y^2+(1/1000000000)*z-25 = 0），why thing like this happen？

when run the order like this, the menu of Plot builder disapper

Thank you in advance for your help

Hi,

I was wondering how I could assign small angel assumptions so that I could simplify an equation of motion to solve for theta double dot. Thank you for your help.

Download small_angle_assumption.mw

Download small_angle_assumption.mw

with(Groebner):
eq1 := a+b*c;
eq2 := a*b*c+a;
eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eliminate([eq1a,eq2a], h);

after eliminate not equal to eq1 and eq2

Hello,

How can I pde with maple?please explain completely,and other question :How can I solve pde with plot in maple because some questions dont have exact answer?

if DegreeLexicographic is T2:=lexdeg([a,b,c],[x,y,z]);

DegreeReverseLexicographic = T2:=lexdeg([c,b,a],[z,y,x])  ?

with(PolynomialIdeals):

quotientlist := Quotient(GB, varj[j]);
finallist2 := [];
for z from 1 to nops(quotientlist) do
if
finallist2 := [op(finallist2), op(z,quotientlist)];
od:

there are only 3 monomials in quotientlist, but nops return 6

If the differential equation has second derivative in the RHS (i.e. in the input), then `StateSpace` gives an error.

I might not be entering it correctly? But if I first create a `TransferFunction` from the ODE, then it works.

Why?

Here is the code:

------------------
restart;
alias(DS=DynamicSystems):
ode2:=diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=diff(u(t),t)+u(t);
sys:=DS:-StateSpace(ode2,'outputvariable'=[y(t)],'inputvariable'=[u(t)]):
-------------------------
Error, (in DynamicSystems:-StateSpace) unable to convert the differential equation system:  invalid form of derivative in differential equation


But now if I do this, it works:

---------------------------------------------
restart;
alias(DS=DynamicSystems):
ode2:=diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=diff(u(t),t)+u(t);
sys:=DS:-TransferFunction(ode2,'outputvariable'=[y(t)],'inputvariable'=[u(t)]):
sys:=DS:-StateSpace(sys);
-----------------------------------------------

Maple 18.01 on windows 7.

Let a finite set of closed intervals in the plane be given.
How to find all the intersections of these, outputing the intersection points together with the intersecting intervals?
This is a problem of computational geometry
(see http://en.wikipedia.org/wiki/Line_segment_intersection).
In other words, how to realize the sweep line algorithm in Maple?

PS. I'd like to note that computational geometry has serious applications, in particular, in robotics.

Good afternoon.

I request your kind suggestion to my above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

I want to solve system of equation but it has unknow parameter.

Then I test system of equation. It hasn't unknowparameter.

eq1 := x^2+y^2 = 4

eq2 := y-x^2 = 0

fsolve({eq1, eq2}, {x, y})

{x = -1.249621068, y = 1.561552813}

So I get answer by using fsolve.

Then I try to put unknow parameter in system of equation.

eq3 := x^2+ky^2 = 4

eq4 := ay-hx^2 = 0

fsolve({eq3, eq4}, {x, y})

Error, (in fsolve) {ay, hx, ky} are in the equation, and are not solved for

I don't get answer and open link. The link hasn't similar this problem.

To motivate some ideas in my research, I've been looking at the expected number of real roots of random polynomials (and their derivatives).  In doing so I have noticed an issue/bug with fsolve and RootFinding[Isolate].  One of the polynomials I came upon was

f(x) = -32829/50000-(9277/50000)*x-(37251/20000)*x^2-(6101/6250)*x^3-(47777/20000)*x^4+(291213/50000)*x^5.

We know that f(x) has at least 1 real root and, in fact, graphing shows that f(x) has exactly 1 real root (~1.018).  However, fsolve(f) and Isolate(f) both return no real roots.  On the other hand, Isolate(f,method=RC) correctly returns the root near 1.018.  I know that fsolve's details page says "It may not return all roots for exceptionally ill-conditioned polynomials", though this system does not seem especially ill-conditioned.  Moreover, Isolate's help page says confidently "All significant digits returned by the program are correct, and unlike purely numerical methods no roots are ever lost, although repeated roots are discarded" which is clearly not the case here.  It also seems interesting that the RealSolving package used by Isolate(f,method=RS) (default method) misses the root while the RegularChains package used by Isolate(f,method=RC) correctly finds the root.

 All-in-all, I am not sure what to make of this.  Is this an issue which has been fixed in more recent incarnations of fsolve or Isolate?  Is this a persistent problem?  Is there a theoretical reason why the root is being missed, particularly for Isolate?

Any help or insight would be greatly appreciated.