7 years, 40 days

## Varying an index in a variable name...

Maple 2015

I am writting a program that needs to rename variables by increasing the second index of a variable, all the variables will be named y[something,number].

e.g.

y[a,2]->y[a,3]

If I was doing this outside maple I can see how I could use regular expressions, but I can't see how to do it in maple

## making a 3d logplot...

Maple 2015

I'd like ot make a 3d graph that is log scaled on at least one of the axis. So far I haven't found a way of doing this that gives a graph that I genuinely like.

The following worksheet shows two ways of making the graph- the first generates the lines on the surface in a very bunched way, the second typesets the tickmarks in a very ugly way.

How can I get a graph with well placed lines and nicely typeset tickmarks?

How do other people make 3d logplots?

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## multivariate partial fractions...

Has anyone been able to do multivariate partial fraction decomposition in maple (here is a paper introducing the idea https://arxiv.org/pdf/1206.4740.pdf)

I often find maple generating complicated rational functions that it would be nice to visualise in other ways

Here is an example of such a function if anyone wants to have a play:

(a*x^3+b*x*y^2+a*x*y+b*y^2)

/(a*x^3+a*b*x*y^2+a*b*y*x^2+b*y^3)

## Minimize the length of an expression...

Maple

Quite often when i use maple I generate expressions that are of vast length, that with a pen and paper can be reduced in length by carefully factorizing, multiplying out and dividing through.

I am wondering if i am missig somethig- if this is a problem all maple users deal with, or if its just a limitation of the program.

Today, maple generated:

d*B[2211](t)/dt = 2*k[a2]*beta*k[d2]*B[2211]*(alpha*beta*R[b]*k[a1]^2+alpha*beta*R[b]*k[a1]*k[a2]+2*alpha*R[b]*k[a1]*k[d1]+2*alpha*R[b]*k[a1]*k[d2]+alpha*R[b]*k[a2]*k[d1]+alpha*R[b]*k[a2]*k[d2]+beta*k[a1]*k[d1]+beta*k[a1]*k[d2]+k[d1]^2+3*k[d1]*k[d2]+2*k[d2]^2)
/(alpha*beta^2*R[b]*k[a1]^2*k[a2]+alpha*beta^2*R[b]*k[a1]*k[a2]^2+alpha*beta*R[b]*k[a1]^2*k[d1]+alpha*beta*R[b]*k[a1]^2*k[d2]+3*alpha*beta*R[b]*k[a1]*k[a2]*k[d1]+3*alpha*beta*R[b]*k[a1]*k[a2]*k[d2]+alpha*beta*R[b]*k[a2]^2*k[d1]+alpha*beta*R[b]*k[a2]^2*k[d2]+alpha*R[b]*k[a1]*k[d1]^2+3*alpha*R[b]*k[a1]*k[d1]*k[d2]+2*alpha*R[b]*k[a1]*k[d2]^2+2*alpha*R[b]*k[a2]*k[d1]^2+3*alpha*R[b]*k[a2]*k[d1]*k[d2]+alpha*R[b]*k[a2]*k[d2]^2+beta^2*k[a1]*k[a2]*k[d1]+beta^2*k[a1]*k[a2]*k[d2]+2*beta*k[a1]*k[d1]^2+3*beta*k[a1]*k[d1]*k[d2]+beta*k[a1]*k[d2]^2+beta*k[a2]*k[d1]^2+3*beta*k[a2]*k[d1]*k[d2]+2*beta*k[a2]*k[d2]^2+2*k[d1]^3+7*k[d1]^2*k[d2]+7*k[d1]*k[d2]^2+2*k[d2]^3)
+(-2*k[d1]-2*k[d2])*B[2211]
+2*k[d1]*B[2211]*(alpha*beta*R[b]*k[a1]*k[a2]+alpha*beta*R[b]*k[a2]^2+alpha*R[b]*k[a1]*k[d1]+alpha*R[b]*k[a1]*k[d2]+2*alpha*R[b]*k[a2]*k[d1]+2*alpha*R[b]*k[a2]*k[d2]+beta*k[a2]*k[d1]+beta*k[a2]*k[d2]+2*k[d1]^2+3*k[d1]*k[d2]+k[d2]^2)*k[a1]*beta
/(alpha*beta^2*R[b]*k[a1]^2*k[a2]+alpha*beta^2*R[b]*k[a1]*k[a2]^2+alpha*beta*R[b]*k[a1]^2*k[d1]+alpha*beta*R[b]*k[a1]^2*k[d2]+3*alpha*beta*R[b]*k[a1]*k[a2]*k[d1]+3*alpha*beta*R[b]*k[a1]*k[a2]*k[d2]+alpha*beta*R[b]*k[a2]^2*k[d1]+alpha*beta*R[b]*k[a2]^2*k[d2]+alpha*R[b]*k[a1]*k[d1]^2+3*alpha*R[b]*k[a1]*k[d1]*k[d2]+2*alpha*R[b]*k[a1]*k[d2]^2+2*alpha*R[b]*k[a2]*k[d1]^2+3*alpha*R[b]*k[a2]*k[d1]*k[d2]+alpha*R[b]*k[a2]*k[d2]^2+beta^2*k[a1]*k[a2]*k[d1]+beta^2*k[a1]*k[a2]*k[d2]+2*beta*k[a1]*k[d1]^2+3*beta*k[a1]*k[d1]*k[d2]+beta*k[a1]*k[d2]^2+beta*k[a2]*k[d1]^2+3*beta*k[a2]*k[d1]*k[d2]+2*beta*k[a2]*k[d2]^2+2*k[d1]^3+7*k[d1]^2*k[d2]+7*k[d1]*k[d2]^2+2*k[d2]^3)

quite clearly there are expressions in there that can be factorised by (k[a1]+k[a2]) and the two quotients have the same denominator. Is there any way of minimizing the length of this expression by factorizing where appropriate, merging denominators when appropriate etc?

## Assume products of variables are zero in...

Maple 2015

I am interested in the behaviour of a system of equations close to the origin- these equations are quite long, and there are a lot of them so i would like to have commands that i can use to assume products of variables are zero.

here are the first two polynomials:

alpha*k[a1]*B[1]^2+(-alpha*k[a1]-alpha*k[a2])*B[2]*B[1]+2*alpha*k[a1]*B[1]*B[11]+alpha*k[a1]*B[12]*B[1]+2*alpha*k[a1]*B[1]*B[211]+alpha*k[a1]*B[221]*B[1]+2*alpha*k[a1]*B[1]*B[2211]+(-alpha*R[b]*k[a1]-k[d1])*B[1]+2*B[11]*k[d1]+B[12]*k[d2]+k[d1]*B[211]+k[d2]*B[221]

(-alpha*k[a1]-alpha*k[a2])*B[2]*B[1]+alpha*k[a2]*B[2]^2+2*alpha*k[a2]*B[2]*B[22]+alpha*B[2]*B[12]*k[a2]+alpha*k[a2]*B[2]*B[211]+2*alpha*k[a2]*B[2]*B[221]+2*alpha*k[a2]*B[2]*B[2211]+(-alpha*R[b]*k[a2]-k[d2])*B[2]+B[12]*k[d1]+2*B[22]*k[d2]+k[d1]*B[211]+k[d2]*B[221]

the varables are the terms with B and a subsript and everything else is a parameter.

My intuition was to use coeffs but I couldn't get anything helpful

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