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MapleSim for Web Converting Systems - Industry...

by: alex_b 85 MapleSim , MapleSim Add-Ons
engineering simulation modeling
26 minutes ago
2  0

Maplesoft continues to bring technology, collaboration, and learning together. Here’s some of the exciting industry news from the world of web converting and high-precision manufacturing lines, and what’s new with MapleSim for Web Converting Systems software.

How is MapleSim helping web converters and manufacturers?

From EV batteries to flexible packaging and medical films, industries that rely on thin web materials are advancing at remarkable speed. To keep pace, engineers need tools that let them model, simulate, and optimize every detail of their process with accuracy and confidence. Processes that once relied on intuition and trial-and-error are now guided by advanced modeling and simulation, such as MapleSim.

Using MapleSim simulation, engineering teams can perform process validation testing virtually - saving time and money compared to physical testing. The virtual models are used to explore and accelerate production — and the new release of MapleSim delivers a powerful set of features to make that possible.

What’s new in the latest MapleSim release?

The new release (available today) enhances MapleSim’s ability to answer “what-if” questions about industrial systems, easily review and compare results, and find strategies to improve production.


For converters and web material manufacturers, it is now even easier to create models of roll-to-roll systems. The updates to MapleSim for web converting systems include pre-built components for modeling spans and applying control during rewinding and matching tension profiles with PLC settings. There is also a new Utilities section to help users to handle sensor data and perform common calculation tasks.

These all reduce the effort to build and update models and add more detail to the simulations. The result: faster to innovate, shorter testing cycles, and more value from every simulation.

You can read more about the MapleSim new features.

Announcing the new Research Partnership Program for MapleSim

We are pleased to announce a new collaboration between Maplesoft and the research teams that are actively advancing converting and web manufacturing processes.
The MapleSim for Web Converting Systems - Research Partnership Program:

  • To support research communities across the web handling industry by providing licenses for MapleSim for Web Converting Systems at NO COST.

Our goal is to equip researchers with the same advanced modeling and simulation tools used in industry, helping them explore new concepts, test ideas, and drive meaningful discoveries.

Focus areas for research include:

  • manufacturing foils, plastic films, non-wovens, and other thin web materials.
  • any specialty process for handling or producing medical equipment, semi-conductors, or EV batteries.

More details of the program and the application process are available on this page.
 

How Simulation Gives You Operational Insights

We have a new web series of articles “R2R Operational Insights” that showcase the ways MapleSim models deliver deeper insights, greater efficiency, and better product quality. These modeling use case articles are sprinkled with customer stories from the world of packaging, EV battery manufacturing, and printing.

You can browse the R2R Operational Insight articles here.

 

Conclusion: Try MapleSim for Yourself

Together, these updates make it easier than ever to simulate, innovate, and learn in web-based manufacturing and design.
-->Start your Free Trial!

 
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Featured Post
Rouben Rostamian
8586

Rupert's cube

It's possible to carve a hole through a unit cube, without splitting it into pieces, so that another unit cube can pass through that hole.  This is know as the Prince Rupert problem and was first analyzed by John Wallis, a contemporary of Isaac Newton.  Here's what the result looks like:

If your computer can play audio, have a look at  Ruperts Cube with music!

Here is the worksheet that produced the cube and the animation: ruperts-cube.mw

October 22
7  2
rupert
Read Full Post

Featured Post
dharr
8687

Solving Diophantine quadratics in two variables

[Edit: a general procedure based on these ideas is given below.]

Maple's isolve can solve some but not all of the quadratic equations in two variables describing the conic sections. Here I show that by transforming the equations, Maple can then solve these missing cases.

> 

restart
> 

with(plots)

I was recently surprised that isolve cannot solve the following simple Diophantine equation

> 

isolve(2*x^2+4*x*y+y^2 = 7)

which has the obvious (to a human) solution {x = 1, y = 1}. This led me to think about the case of conic sections, which have the following general equation (= 0 implied), where I assume a, () .. (), f are integers.

> 

P := a*x^2+b*x*y+c*y^2+d*x+e*y+f

a*x^2+b*x*y+c*y^2+d*x+e*y+f

The above equation has discriminant -4*a*c+b^2 positive, indicating that is is a hyperbola.

> 

h_params := {a = 2, b = 4, c = 1, d = 0, e = 0, f = -7}; P__h := eval(P, h_params); disc := -4*a*c+b^2; eval(disc, h_params); plot__h := implicitplot(P__h, x = -10 .. 10, y = -10 .. 10, colour = red)

{a = 2, b = 4, c = 1, d = 0, e = 0, f = -7}

2*x^2+4*x*y+y^2-7

-4*a*c+b^2

8

Here's a parabola case (discriminant = 0) that isolve also has trouble with

> 

p_params := {a = 2, b = 4, c = 2, d = 1, e = 2, f = 7}; eval(disc, p_params); P__p := eval(P, p_params); {isolve(P__p)}; plot__h := implicitplot(P__p, x = -10 .. 10, y = -10 .. 10, colour = red)

{a = 2, b = 4, c = 2, d = 1, e = 2, f = 7}

0

2*x^2+4*x*y+2*y^2+x+2*y+7

{}

But this has at least one solution

> 

eval(P__p, {x = 7, y = -7})

0

Maple seems to do better in the elliptic case (discriminant negative) and finds two solutions. Examination of the plot suggests there are no other solutions.

> 

e_params := {a = 2, b = 4, c = 3, d = 1, e = 2, f = -7}; eval(disc, e_params); P__e := eval(P, e_params); {isolve(P__e)}; plot__e := implicitplot(P__e, x = -10 .. 10, y = -10 .. 10, colour = red)

{a = 2, b = 4, c = 3, d = 1, e = 2, f = -7}

-8

2*x^2+4*x*y+3*y^2+x+2*y-7

{{x = -3, y = 2}, {x = 2, y = -3}}

I show that transformation of the general equation to the form -D*Y^2+X^2 = m, where D is the discriminant, allows Maple to solve the hyperbolic case, as well as the elliptic case it already knows how to solve; another transformation works for the parabolic case. Maple appears to be able to solve all (solvable) cases of the transformed equations, though this is not clear from the help page. The transformation is discussed in Bogdan Grechuk, Polynomial Diophantine Equations: A Systematic Approach, Springer, 2024, Sec. 3.1.7. doi: 10.1007/978-3-031-62949-5

 

A complete classification of the conics, including degenerate cases, is given in https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections. If the determinant, delta, of the following matrix is zero, we have a degenerate case.

> 

A__Q := Matrix(3, 3, [a, (1/2)*b, (1/2)*d, (1/2)*b, c, (1/2)*e, (1/2)*d, (1/2)*e, f]); delta := LinearAlgebra:-Determinant(A__Q)

Matrix(%id = 36893489963432522084)

a*c*f-(1/4)*a*e^2-(1/4)*b^2*f+(1/4)*b*d*e-(1/4)*c*d^2

The case of a = b and b = c and c = 0 is just the linear case, which Maple can solve, and is one case where D = delta and delta = 0. Other degenerate parabola cases are two coincident lines or two parallel lines. Degenerate hyperbolas are two intersecting lines, and degenerate ellipses are a single point. Maple can solve all these cases, e.g.,NULL

> 

expand((2*x+3*y+1)*(2*x+3*y)); {isolve(%)}; expand((2*x+3*y)*(2*x+3*y)); {isolve(%)}; expand((x-2)*(y-3)); {isolve(%)}; x^2+y^2 = 0; {isolve(%)}

4*x^2+12*x*y+9*y^2+2*x+3*y

{{x = -3*_Z1, y = 2*_Z1}, {x = -2-3*_Z1, y = 1+2*_Z1}}

4*x^2+12*x*y+9*y^2

{{x = -3*_Z1, y = 2*_Z1}}

x*y-3*x-2*y+6

{{x = _Z1, y = 3}}

x^2+y^2 = 0

{{x = 0, y = 0}}

(The intersecting lines case above only finds one of the lines.) The transformation will consider only the case where at least one of a or c is non-zero. This misses hyperbolas with a = c and c = 0; Maple seems to handle these bilinear equations, e.g.,

> 

bl_params := {a = 0, b = 2, c = 0, d = 1, e = 1, f = 2}; P__bl := eval(P, bl_params); {isolve(P__bl)}

{a = 0, b = 2, c = 0, d = 1, e = 1, f = 2}

2*x*y+x+y+2

{{x = -2, y = 0}, {x = -1, y = 1}, {x = 0, y = -2}, {x = 1, y = -1}}

Transformation for non-zero discriminant
At least one of a or c must be non-zero; if necessary exchange x and y to ensure a is non-zero.

We multiply P by -4*a*(-4*a*c+b^2) and change to new variables X and Y.

> 

itr := {X = (-4*a*c+b^2)*y+b*d-2*a*e, Y = 2*a*x+b*y+d}; tr := solve(itr, {x, y})

{X = (-4*a*c+b^2)*y+b*d-2*a*e, Y = 2*a*x+b*y+d}

{x = (1/2)*(4*Y*a*c-Y*b^2+2*a*b*e-4*a*c*d+X*b)/((4*a*c-b^2)*a), y = -(2*a*e-b*d+X)/(4*a*c-b^2)}

The transformed equation has the form -D*Y^2+X^2-m = 0 or -D*Y^2+X^2 = m, where D is the discriminant.

> 

Q := collect(normal(eval(-4*P*a*(-4*a*c+b^2), tr)), {X, Y}); m := -coeff(coeff(Q, X, 0), Y, 0)

X^2+(4*a*c-b^2)*Y^2+16*a^2*c*f-4*a^2*e^2-4*a*b^2*f+4*a*b*d*e-4*a*c*d^2

-16*a^2*c*f+4*a^2*e^2+4*a*b^2*f-4*a*b*d*e+4*a*c*d^2

For positive discriminant D, this is a general Pell's equation, -D*Y^2+X^2 = m, which Maple knows how to solve. (The definition of Pell's equation requires that D is not a square, but Maple can also solve the simpler case where D is a square.) For the hyperbola above, we have an infinite number of solutions, parameterized by an arbitrary integer _Z1.

> 

Q__h := eval(Q, h_params); solXY__h := {isolve(Q__h)}

X^2-8*Y^2+448

{{X = -12*(1+2^(1/2))^(1+2*_Z1)-12*(1-2^(1/2))^(1+2*_Z1)-4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = -3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))-2*(1+2^(1/2))^(1+2*_Z1)-2*(1-2^(1/2))^(1+2*_Z1)}, {X = -12*(1+2^(1/2))^(1+2*_Z1)-12*(1-2^(1/2))^(1+2*_Z1)-4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = 3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))+2*(1+2^(1/2))^(1+2*_Z1)+2*(1-2^(1/2))^(1+2*_Z1)}, {X = -12*(1+2^(1/2))^(1+2*_Z1)-12*(1-2^(1/2))^(1+2*_Z1)+4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = -3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))+2*(1+2^(1/2))^(1+2*_Z1)+2*(1-2^(1/2))^(1+2*_Z1)}, {X = -12*(1+2^(1/2))^(1+2*_Z1)-12*(1-2^(1/2))^(1+2*_Z1)+4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = 3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))-2*(1+2^(1/2))^(1+2*_Z1)-2*(1-2^(1/2))^(1+2*_Z1)}, {X = 12*(1+2^(1/2))^(1+2*_Z1)+12*(1-2^(1/2))^(1+2*_Z1)-4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = -3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))+2*(1+2^(1/2))^(1+2*_Z1)+2*(1-2^(1/2))^(1+2*_Z1)}, {X = 12*(1+2^(1/2))^(1+2*_Z1)+12*(1-2^(1/2))^(1+2*_Z1)-4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = 3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))-2*(1+2^(1/2))^(1+2*_Z1)-2*(1-2^(1/2))^(1+2*_Z1)}, {X = 12*(1+2^(1/2))^(1+2*_Z1)+12*(1-2^(1/2))^(1+2*_Z1)+4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = -3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))-2*(1+2^(1/2))^(1+2*_Z1)-2*(1-2^(1/2))^(1+2*_Z1)}, {X = 12*(1+2^(1/2))^(1+2*_Z1)+12*(1-2^(1/2))^(1+2*_Z1)+4*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), Y = 3*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))+2*(1+2^(1/2))^(1+2*_Z1)+2*(1-2^(1/2))^(1+2*_Z1)}}

Transforming back to the original coordinates

> 

sol__h := {seq(eval(eval(tr, h_params), solXY), `in`(solXY, solXY__h))}

{{x = -2*(1+2^(1/2))^(1+2*_Z1)-2*(1-2^(1/2))^(1+2*_Z1)-(5/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = (3/2)*(1+2^(1/2))^(1+2*_Z1)+(3/2)*(1-2^(1/2))^(1+2*_Z1)+(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = -2*(1+2^(1/2))^(1+2*_Z1)-2*(1-2^(1/2))^(1+2*_Z1)+(5/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = (3/2)*(1+2^(1/2))^(1+2*_Z1)+(3/2)*(1-2^(1/2))^(1+2*_Z1)-(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = -(1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)-(1/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = (3/2)*(1+2^(1/2))^(1+2*_Z1)+(3/2)*(1-2^(1/2))^(1+2*_Z1)-(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = -(1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)+(1/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = (3/2)*(1+2^(1/2))^(1+2*_Z1)+(3/2)*(1-2^(1/2))^(1+2*_Z1)+(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = (1+2^(1/2))^(1+2*_Z1)+(1-2^(1/2))^(1+2*_Z1)-(1/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = -(3/2)*(1+2^(1/2))^(1+2*_Z1)-(3/2)*(1-2^(1/2))^(1+2*_Z1)-(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = (1+2^(1/2))^(1+2*_Z1)+(1-2^(1/2))^(1+2*_Z1)+(1/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = -(3/2)*(1+2^(1/2))^(1+2*_Z1)-(3/2)*(1-2^(1/2))^(1+2*_Z1)+(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = 2*(1+2^(1/2))^(1+2*_Z1)+2*(1-2^(1/2))^(1+2*_Z1)-(5/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = -(3/2)*(1+2^(1/2))^(1+2*_Z1)-(3/2)*(1-2^(1/2))^(1+2*_Z1)+(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}, {x = 2*(1+2^(1/2))^(1+2*_Z1)+2*(1-2^(1/2))^(1+2*_Z1)+(5/4)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1)), y = -(3/2)*(1+2^(1/2))^(1+2*_Z1)-(3/2)*(1-2^(1/2))^(1+2*_Z1)-(1/2)*2^(1/2)*((1+2^(1/2))^(1+2*_Z1)-(1-2^(1/2))^(1+2*_Z1))}}

Evaluate for some _Z1 values, say _Z1=0 and _Z1=5.
It is evident from tr above that integer solutions in X, Y may transform to non-integer solutions in x, y but that doesn't occur for these two cases

> 

sol__h0 := evala(eval(sol__h, _Z1 = 0)); sol__h5 := evala(eval(sol__h, _Z1 = 5))

{{x = -9, y = 5}, {x = -3, y = 1}, {x = -1, y = -1}, {x = -1, y = 5}, {x = 1, y = -5}, {x = 1, y = 1}, {x = 3, y = -1}, {x = 9, y = -5}}

{{x = -61181, y = 35839}, {x = -21979, y = 12875}, {x = -10497, y = 35839}, {x = -3771, y = 12875}, {x = 3771, y = -12875}, {x = 10497, y = -35839}, {x = 21979, y = -12875}, {x = 61181, y = -35839}}

Check they are solutions to P__h

> 

map2(eval, P__h, `union`(sol__h0, sol__h5))

{0}

For negative discriminant and negative m, the equation -D*Y^2+X^2 = m has no solutions. In the classification scheme for the conics, the "imaginary ellipse" case (no real solutions) occurs when (a+c)*delta > 0. For negative discriminant, we must have a and c the same sign, and this is the case of negative m.

> 

factor(expand((16*(a+c))*delta)); factor(-m)

4*(a+c)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)

4*a*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)

. In this case Maple returns NULL for both the untransformed and transformed case, which can mean no solutions or just that isolve couldn't find any.

> 

ie_params := {a = 3, b = 0, c = 5, d = 0, e = 0, f = 8}; P__ie := eval(P, ie_params); {isolve(P__ie)}; Q__ie := eval(Q, ie_params); {isolve(Q__ie)}

{a = 3, b = 0, c = 5, d = 0, e = 0, f = 8}

3*x^2+5*y^2+8

{}

X^2+60*Y^2+5760

{}

For negative discriminant and positive m or (a+c)*delta < 0, the ellipse is real, and there are a finite number of solutions. Maple solves the untransformed and transformed equations.
Here we need to filter out non-integer solutions

> 

P__e; {isolve(P__e)}; Q__e := eval(Q, e_params); solXY__e := {isolve(Q__e)}; {seq(eval(eval(tr, e_params), solXY), `in`(solXY, solXY__e))}; sol__e := select(proc (q) options operator, arrow; eval(x::integer, q) and eval(y::integer, q) end proc, %)

2*x^2+4*x*y+3*y^2+x+2*y-7

{{x = -3, y = 2}, {x = 2, y = -3}}

X^2+8*Y^2-472

{{X = -20, Y = -3}, {X = -20, Y = 3}, {X = 20, Y = -3}, {X = 20, Y = 3}}

{{x = -3, y = 2}, {x = 2, y = -3}, {x = -3/2, y = 2}, {x = 7/2, y = -3}}

{{x = -3, y = 2}, {x = 2, y = -3}}

Transformation for zero discriminant
For the case of zero discriminant (parabola), we need a different transformation.

> 

itr0 := {X = 2*a*x+b*y+d, Y = y}; tr0 := solve(itr0, {x, y})

{X = 2*a*x+b*y+d, Y = y}

{x = (1/2)*(-Y*b+X-d)/a, y = Y}

The transformed equation is of the form A*Y+X^2+B = 0

> 

Q0 := collect(normal(eval(4*a*P, tr0)), {X, Y})

X^2+(4*a*c-b^2)*Y^2+(4*a*e-2*b*d)*Y+4*f*a-d^2

We consider the parabolic example above, for which Maple finds no solutions without transformation.

> 

P__p; {isolve(P__p)}

2*x^2+4*x*y+2*y^2+x+2*y+7

{}

For the transformed problem, Maple finds an infinite number of solutions

> 

Q__p := eval(Q0, p_params); solXY__p := {isolve(Q__p)}; sol__p := {seq(eval(eval(tr0, p_params), solXY), `in`(solXY, solXY__p))}

X^2+8*Y+55

{{X = 1+8*_Z1, Y = -8*_Z1^2-2*_Z1-7}, {X = 3+8*_Z1, Y = -8*_Z1^2-6*_Z1-8}, {X = 5+8*_Z1, Y = -8*_Z1^2-10*_Z1-10}, {X = 7+8*_Z1, Y = -8*_Z1^2-14*_Z1-13}}

{{x = 17/2+8*_Z1+8*_Z1^2, y = -8*_Z1^2-6*_Z1-8}, {x = 29/2+16*_Z1+8*_Z1^2, y = -8*_Z1^2-14*_Z1-13}, {x = 8*_Z1^2+4*_Z1+7, y = -8*_Z1^2-2*_Z1-7}, {x = 8*_Z1^2+12*_Z1+11, y = -8*_Z1^2-10*_Z1-10}}

Two of the general solutions will not give integer solutions, so could be filtered out, but it is easier to filter after choosing some specific _Z1 values.

> 

eval(sol__p, _Z1 = 0); sol__p0 := select(proc (q) options operator, arrow; eval(x::integer, q) and eval(y::integer, q) end proc, %); eval(sol__p, _Z1 = 5); sol__p5 := select(proc (q) options operator, arrow; eval(x::integer, q) and eval(y::integer, q) end proc, %)

{{x = 7, y = -7}, {x = 11, y = -10}, {x = 17/2, y = -8}, {x = 29/2, y = -13}}

{{x = 7, y = -7}, {x = 11, y = -10}}

{{x = 227, y = -217}, {x = 271, y = -260}, {x = 497/2, y = -238}, {x = 589/2, y = -283}}

{{x = 227, y = -217}, {x = 271, y = -260}}

Check they are solutions to P__p

> 

map2(eval, P__p, `union`(sol__p0, sol__p5))

{0}

> 

NULL

Download DiophantineConics2.mw

October 31
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    what is the *fundamental* difference between ...

    Maple asked by Jean-Miche... 50 November 10
    2  6
    subscript indexing

    misinterpretation of units

    Maple 2025 asked by PerKirkega... 25 Yesterday
    1  2
    units incomplete-question

    comparing solutions of an ode

    Maple asked by awass 316 Yesterday
    1  11
    ode dsolve numeric differential-equations plotting

    where is problem why i can't find my paramete...

    Maple 2024 asked by Math-dasht... 130 Today
    1  4
    solve

    How make thus point be simpler than the exact...

    Maple 2024 asked by Math-dasht... 130 Yesterday
    0  7
    parameter differential-equations phaseportrait plotting incomplete-question

    syntax error using union

    Maple 2019 asked by Andiguys 85 Yesterday
    0  1
    syntax union set duplicate-question

    2D plot of multiple inequalities or maximum

    Maple 2019 asked by Andiguys 85 November 11
    0  6
    inequality plotting

    How to delete this interactive plot builder call

    Maple 2025 asked by C_R 3527 November 10
    0  2
    plotbuilder

    How to show 3D surface plot shadow at the base?

    Maple 2025 asked by AHSAN 160 November 10
    0  13
    contourplot numeric plot3d surface 3d differential-equations bvp plotting contourplot3d