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en-us2023 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 24 Mar 2023 15:38:18 GMTFri, 24 Mar 2023 15:38:18 GMTMaple Questions and Posts on MaplePrimeshttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Maple Posts and Questions
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Is there a problem with Maple 2023 and plotting 3D figures?
https://www.mapleprimes.com/questions/235995-Is-There-A-Problem-With-Maple-2023-And?ref=Feed:MaplePrimes:Tagged With Maple
<p>Hello</p>
<p>I am running Maple 2023 on a mac M1. When I ask Maple to print a document with 3D figures, only the axes come out. 2D figures come out fine. If I do the same thing on Maple 2022 on the same machine, there is no problem at all. </p>
<p><img height="100px" src="/view.aspx?sf=235995_question/Fig_3D_Maple2023.png" width="100px"></p>
<p><img src="/view.aspx?sf=235995_question/Fig_3D_Maple2023.png" style="height: 2px; width: 2px;"> <img height="100px" src="/view.aspx?sf=235995_question/Fig_3D_Maple2022.png" width="100px"></p>
<p>Can any one confirm this problem?</p>
<p>many thanks</p>
<p>Hello</p>
<p>I am running Maple 2023 on a mac M1. When I ask Maple to print a document with 3D figures, only the axes come out. 2D figures come out fine. If I do the same thing on Maple 2022 on the same machine, there is no problem at all. </p>
<p><img height="100px" src="/view.aspx?sf=235995_question/Fig_3D_Maple2023.png" width="100px" /></p>
<p><img src="/view.aspx?sf=235995_question/Fig_3D_Maple2023.png" style="height: 2px; width: 2px;" /> <img height="100px" src="/view.aspx?sf=235995_question/Fig_3D_Maple2022.png" width="100px" /></p>
<p>Can any one confirm this problem?</p>
<p>many thanks</p>
235995Fri, 24 Mar 2023 11:33:50 ZemendesemendesA simple question about sets
https://www.mapleprimes.com/questions/235994-A-Simple-Question-About-Sets?ref=Feed:MaplePrimes:Tagged With Maple
<p>When we specify a set (a sequence of objects enclosed in curly braces), Maple removes duplicates, since the elements of the set must be unique, that is, they cannot be repeated. See below for 2 examples. With the first example {<strong>a<=b</strong> and <strong>b>=a}</strong>, everything is in order, since they are one and the same. But Maple treats the same equality, written in two ways <strong> {a=b, b=a}</strong> , as different objects. It seems to me that this is not very convenient:</p>
<pre class="prettyprint">
restart;
{a<=b, b>=a}; # OK
{a=b, b=a}; # not OK
is((a=b)=(b=a)); # not OK
</pre>
<p> <img src="/view.aspx?sf=235994_question/1.png" style="height: 80px; width: 150px;"></p>
<p> </p>
<p>When we specify a set (a sequence of objects enclosed in curly braces), Maple removes duplicates, since the elements of the set must be unique, that is, they cannot be repeated. See below for 2 examples. With the first example {<strong>a<=b</strong> and <strong>b>=a}</strong>, everything is in order, since they are one and the same. But Maple treats the same equality, written in two ways <strong> {a=b, b=a}</strong> , as different objects. It seems to me that this is not very convenient:</p>
<pre class="prettyprint">
restart;
{a<=b, b>=a}; # OK
{a=b, b=a}; # not OK
is((a=b)=(b=a)); # not OK
</pre>
<p> <img src="/view.aspx?sf=235994_question/1.png" style="height: 80px; width: 150px;" /></p>
<p> </p>
235994Fri, 24 Mar 2023 09:59:39 ZKitonumKitonumComputing very high genus
https://www.mapleprimes.com/questions/235993-Computing-Very-High-Genus?ref=Feed:MaplePrimes:Tagged With Maple
<p>Hi,</p>
<p>Would anyone here be interested in helping me with a genus problem and running the following code and letting me know the genus? I do not have Maple and have tried other avenues for help without success; the on-line Magma calculator cannot compute it and Mathematica does not have a genus function. I believe the following is the correct syntax to compute the genus however it may take a while.</p>
<p> </p>
<p>with(algcurves);</p>
<p>f:=2*z^6 + z^7/2 - (5*z^11)/4 + 4*z^22 + (29*z^34)/10 - z^40 - (13*z^43)/2 + w^38*(z^2 - z^7/4) + <br>
w^49*(-z^9 + z^13/4 + 2*z^14) + w^34*((7*z^14)/3 - (3*z^18)/2) + w^47*(z^10/3 + (7*z^11)/4 + (8*z^21)/5) + <br>
w^24*(4*z^8 + (4*z^25)/5 - (3*z^27)/2) + w^9*((-6*z^2)/5 - z^6/2 + (7*z^31)/3) + <br>
w^16*((7*z^21)/3 + (4*z^27)/5 + (4*z^32)/3) + w^18*(-6*z^14 - 2*z^31 - z^33) + w^3*(2*z^17 + (7*z^34)/2) + <br>
w^16*((-3*z^5)/4 - 2*z^36 + z^39/3) + w^50*(-1/3*z^23 - (7*z^40)/2 + z^42) + w^4*((-3*z^30)/2 + (4*z^38)/3 + (8*z^42)/5) + <br>
w^33*(-3*z^4 + (8*z^22)/3 - (8*z^43)/5) + w^16*(-1/4*z^26 - (3*z^41)/4 - z^43) + w^48*((2*z^2)/3 + 6*z^26 + (3*z^43)/5) + <br>
w^49*(2*z^18 + z^36 - 2*z^44) + w^10*((-2*z^11)/5 - (3*z^26)/2 + z^45) + w^40*(-1/2*z^20 - z^29 + z^46) + <br>
w^36*(-4 + 8*z^13 - (7*z^47)/4) + w^14*((7*z^24)/5 - 6*z^32 - 6*z^49) + w^22*(-2*z^27 - (8*z^50)/3) + <br>
w^2*((3*z^10)/5 + (7*z^24)/4 - z^50/4);</p>
<p>genus(f,z,w)</p>
<p>Hi,</p>
<p>Would anyone here be interested in helping me with a genus problem and running the following code and letting me know the genus? I do not have Maple and have tried other avenues for help without success; the on-line Magma calculator cannot compute it and Mathematica does not have a genus function. I believe the following is the correct syntax to compute the genus however it may take a while.</p>
<p> </p>
<p>with(algcurves);</p>
<p>f:=2*z^6 + z^7/2 - (5*z^11)/4 + 4*z^22 + (29*z^34)/10 - z^40 - (13*z^43)/2 + w^38*(z^2 - z^7/4) + <br />
w^49*(-z^9 + z^13/4 + 2*z^14) + w^34*((7*z^14)/3 - (3*z^18)/2) + w^47*(z^10/3 + (7*z^11)/4 + (8*z^21)/5) + <br />
w^24*(4*z^8 + (4*z^25)/5 - (3*z^27)/2) + w^9*((-6*z^2)/5 - z^6/2 + (7*z^31)/3) + <br />
w^16*((7*z^21)/3 + (4*z^27)/5 + (4*z^32)/3) + w^18*(-6*z^14 - 2*z^31 - z^33) + w^3*(2*z^17 + (7*z^34)/2) + <br />
w^16*((-3*z^5)/4 - 2*z^36 + z^39/3) + w^50*(-1/3*z^23 - (7*z^40)/2 + z^42) + w^4*((-3*z^30)/2 + (4*z^38)/3 + (8*z^42)/5) + <br />
w^33*(-3*z^4 + (8*z^22)/3 - (8*z^43)/5) + w^16*(-1/4*z^26 - (3*z^41)/4 - z^43) + w^48*((2*z^2)/3 + 6*z^26 + (3*z^43)/5) + <br />
w^49*(2*z^18 + z^36 - 2*z^44) + w^10*((-2*z^11)/5 - (3*z^26)/2 + z^45) + w^40*(-1/2*z^20 - z^29 + z^46) + <br />
w^36*(-4 + 8*z^13 - (7*z^47)/4) + w^14*((7*z^24)/5 - 6*z^32 - 6*z^49) + w^22*(-2*z^27 - (8*z^50)/3) + <br />
w^2*((3*z^10)/5 + (7*z^24)/4 - z^50/4);</p>
<p>genus(f,z,w)</p>
235993Fri, 24 Mar 2023 09:42:48 ZjackTempletonjackTempletonDifficulty with pdsolve and electromagnetics
https://www.mapleprimes.com/questions/235992-Difficulty-With-Pdsolve-And-Electromagnetics?ref=Feed:MaplePrimes:Tagged With Maple
<p><a href="/view.aspx?sf=235992_question/perturb_mag_current_density_2.mw">perturb_mag_current_density_2.mw</a></p>
<p>I am trying to calculate the electric field E induced in a vibrating cantilever of conductive material, oscillating in the field of a permanent magnet. However, I am having some difficulty getting pdsolve to work the way I want it to. I'm also not sure if the partial differential eqations I derived from Maxwell's equations are correct, or if the boundary conditions for the electric field in the cantilever are correct. Currently pdsolve gives me no solutions, which makes me think that either my PDEs or my BCs are not correct. It may be that I need to try some sort of numerical method as well. I am assuming that the z component of the electric field is just 0. My third PDE comes from setting the divergence of the electric field to 0. My first two PDEs come from the vector laplacian and its relation to the divergence and curl:</p>
<p>Laplacian * E = Div(E) -Curl(Curl(E))</p>
<p>The x and y components of this should be my first and second PDE, respectively. Note that in this equation the divergence of E is 0, and the curl of E is -dB/dt, where B is the magnetic field.</p>
<p>My boundary conditions are simply that the components of the electric field at the surface of the cantilever is always tangent to the surface.</p>
<p>I have tried various simplifications, such as setting the right hand side of the PDEs to 0, and still I don't get any solution.</p>
<p>My question: Are my PDEs and BCs sensible? And if so, what do I need to do with pdsolve to get a proper solution?</p>
<p><a href="/view.aspx?sf=235992_question/perturb_mag_current_density_2.mw">perturb_mag_current_density_2.mw</a></p>
<p>I am trying to calculate the electric field E induced in a vibrating cantilever of conductive material, oscillating in the field of a permanent magnet. However, I am having some difficulty getting pdsolve to work the way I want it to. I'm also not sure if the partial differential eqations I derived from Maxwell's equations are correct, or if the boundary conditions for the electric field in the cantilever are correct. Currently pdsolve gives me no solutions, which makes me think that either my PDEs or my BCs are not correct. It may be that I need to try some sort of numerical method as well. I am assuming that the z component of the electric field is just 0. My third PDE comes from setting the divergence of the electric field to 0. My first two PDEs come from the vector laplacian and its relation to the divergence and curl:</p>
<p>Laplacian * E = Div(E) -Curl(Curl(E))</p>
<p>The x and y components of this should be my first and second PDE, respectively. Note that in this equation the divergence of E is 0, and the curl of E is -dB/dt, where B is the magnetic field.</p>
<p>My boundary conditions are simply that the components of the electric field at the surface of the cantilever is always tangent to the surface.</p>
<p>I have tried various simplifications, such as setting the right hand side of the PDEs to 0, and still I don't get any solution.</p>
<p>My question: Are my PDEs and BCs sensible? And if so, what do I need to do with pdsolve to get a proper solution?</p>
235992Thu, 23 Mar 2023 19:45:10 ZjbromelljbromellHow to find roots of polynomials with a huge Groebner basis?
https://www.mapleprimes.com/questions/235991-How-To-Find-Roots-Of-Polynomials-With?ref=Feed:MaplePrimes:Tagged With Maple
<p>Hi everyone,</p>
<p>I am trying to find the roots of a system of 3 multivariate polynomials with 3 variables. I have used</p>
<p>G := Basis(P, tdeg(x6, x7, x8))</p>
<p>from the Groebner package and got a Groebner Basis with 29 elements (the length of output exceeds the limit). I want to find roots in the interval [0,1] with x<y<z. Is there a way to find solutions? Some of the polynomials in the Basis are of order 11 and I can't find a single variable polynomial in the basis. Is there an efficiet way to find such roots? Or should I do someting completely different?</p>
<p>Best</p>
<p>fabs</p>
<p>Hi everyone,</p>
<p>I am trying to find the roots of a system of 3 multivariate polynomials with 3 variables. I have used</p>
<p>G := Basis(P, tdeg(x6, x7, x8))</p>
<p>from the Groebner package and got a Groebner Basis with 29 elements (the length of output exceeds the limit). I want to find roots in the interval [0,1] with x<y<z. Is there a way to find solutions? Some of the polynomials in the Basis are of order 11 and I can't find a single variable polynomial in the basis. Is there an efficiet way to find such roots? Or should I do someting completely different?</p>
<p>Best</p>
<p>fabs</p>
235991Thu, 23 Mar 2023 17:25:54 ZfabsfabsHow can I implement a simple code to obtain the dimension and basis in the quotient ring by {\tt Maple}?
https://www.mapleprimes.com/questions/235990-How-Can-I-Implement-A-Simple-Code-To?ref=Feed:MaplePrimes:Tagged With Maple
<p>Let us consider the following assumptions:</p>
<p>Any set of binomials $B \in R=K[x_1, \cdots, x_n]$ induces an equivalence relation on the set of monomials in $R$ under which $m_1∼m_2$ if and only if $m_1−tm_2\in \langle B \rangle$ for some non-zero $t\in K$. As a k-vector space, the quotient ring $R/B$ s spanned by the equivalence classes of monomials. Now let $f =x^2−y^2$ be a binomial in $K[x, y]$. Among monomials of total degree three, $x^3$ and $xy^2$, as well as $x^2y$ and $y^3$ become equal in $K[x, y] / \langle f\rangle$.</p>
<p>Why the degree three part in the quotient is two-dimensional with one basis vector per equivalence class?</p>
<p>Also, why does the polynomial $f=x^3+xy^2+y^3$ map to a binomial with a coefficient matrix [2, 1]? I think this matrix arises from the matrix [1, 1, 1, 0] by summing the columns corresponding to $x^3$ and $xy^2$ and those for $x^2y$ and $y^3$. </p>
<p>How can I implement a simple code to obtain these results in {\tt Maple}?</p>
<p>I am looking forward to hearing any help and guidance.</p>
<p>Thank you in advance</p>
<p>Let us consider the following assumptions:</p>
<p>Any set of binomials $B \in R=K[x_1, \cdots, x_n]$ induces an equivalence relation on the set of monomials in $R$ under which $m_1∼m_2$ if and only if $m_1−tm_2\in \langle B \rangle$ for some non-zero $t\in K$. As a k-vector space, the quotient ring $R/B$ s spanned by the equivalence classes of monomials. Now let $f =x^2−y^2$ be a binomial in $K[x, y]$. Among monomials of total degree three, $x^3$ and $xy^2$, as well as $x^2y$ and $y^3$ become equal in $K[x, y] / \langle f\rangle$.</p>
<p>Why the degree three part in the quotient is two-dimensional with one basis vector per equivalence class?</p>
<p>Also, why does the polynomial $f=x^3+xy^2+y^3$ map to a binomial with a coefficient matrix [2, 1]? I think this matrix arises from the matrix [1, 1, 1, 0] by summing the columns corresponding to $x^3$ and $xy^2$ and those for $x^2y$ and $y^3$. </p>
<p>How can I implement a simple code to obtain these results in {\tt Maple}?</p>
<p>I am looking forward to hearing any help and guidance.</p>
<p>Thank you in advance</p>
235990Thu, 23 Mar 2023 17:06:12 ZMDDMDD