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en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 26 Jan 2022 17:06:37 GMTWed, 26 Jan 2022 17:06:37 GMTThe latest posts added to MaplePrimeshttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Newest Posts
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Polynomial Ideals Usage
https://www.mapleprimes.com/posts/216601-Polynomial-Ideals-Usage?ref=Feed:MaplePrimes:New Posts
<p>Our user wondered about using PolynomialIdeals:</p>
<p>1. If we have n+1 polynomials, f, g1,...,gn, how to determine if f is in the ideal generated by g1,...,gn?</p>
<p>2. If so, how to write f as a polynomial combination of g1,...,gn? </p>
<p>We suggested that;</p>
<p>The nicest interface to answer the first question is given by the <a href='http://www.maplesoft.com/support/help/search.aspx?term=PolynomialIdeals,Operators' target='_new'>?PolynomialIdeals,Operators</a> page: you can write</p>
<pre>
with(PolynomialIdeals):
with(Operators):
J := <g1, g2, ..., gn>;
f in J; # true or false
</pre>
<p>To answer the second question, you need to use the lower level package (which underlies the package). This will also answer the first question for you. In particular the command. You can write:</p>
<pre>
with(Groebner):
G := [g1, g2, ..., gn];
ord := tdeg(x,y,z); # replace x, y, z with the appropriate variables; you can also use other variable orders -- see <a href='http://www.maplesoft.com/support/help/search.aspx?term=Groebner,MonomialOrders
' target='_new'>?Groebner,MonomialOrders
</a>
b := Basis(G, ord);
n := NormalForm(f, b, ord, 'Q');
# if n = 0 then f is in the ideal; Q is the list of coefficients:
f - add(Q[i] * G[i], i = 1 .. numelems(b)); # this will be equal to n.</pre>
<p>Our user wondered about using PolynomialIdeals:</p>
<p>1. If we have n+1 polynomials, f, g1,...,gn, how to determine if f is in the ideal generated by g1,...,gn?</p>
<p>2. If so, how to write f as a polynomial combination of g1,...,gn? </p>
<p>We suggested that;</p>
<p>The nicest interface to answer the first question is given by the ?PolynomialIdeals,Operators page: you can write</p>
<pre>
with(PolynomialIdeals):
with(Operators):
J := <g1, g2, ..., gn>;
f in J; # true or false
</pre>
<p>To answer the second question, you need to use the lower level <tt>Groebner</tt> package (which underlies the <tt>PolynomialIdeals</tt> package). This will also answer the first question for you. In particular the <tt>NormalForm</tt> command. You can write:</p>
<pre>
with(Groebner):
G := [g1, g2, ..., gn];
ord := tdeg(x,y,z); # replace x, y, z with the appropriate variables; you can also use other variable orders -- see ?Groebner,MonomialOrders
b := Basis(G, ord);
n := NormalForm(f, b, ord, 'Q');
# if n = 0 then f is in the ideal; Q is the list of coefficients:
f - add(Q[i] * G[i], i = 1 .. numelems(b)); # this will be equal to n.</pre>
216601Fri, 21 Jan 2022 17:08:18 ZTechnicalSupportTechnicalSupportWhat Are Your Favourite Maple Learn Tricks?
https://www.mapleprimes.com/maplesoftblog/216582-What-Are-Your-Favourite-Maple-Learn-Tricks?ref=Feed:MaplePrimes:New Posts
<p>I’m looking for users’ favourite tips and tricks in <a href="http://learn.maplesoft.com">Maple Learn</a>. Specifically, small pieces of advice that most people don’t know about, but that helped you create better Maple Learn documents. For instance,</p>
<ul>
<li style="margin-left: 36pt;">A favorite feature that you think is hard to discover;</li>
<li style="margin-left: 36pt;">Common techniques you use when creating documents;</li>
<li style="margin-left: 36pt;">Things about Maple Learn you wish you knew when you started.</li>
</ul>
<p>These tricks could be for newbies or for experienced users.</p>
<p>To start off the discussion, let me share three of my own favorite tricks in Maple Learn.</p>
<p><strong>1. Using Documents from the Document Gallery</strong></p>
<p>Writing a Maple Learn document from scratch can seem overwhelming, especially for beginners. A much easier way to create documents is to start with a template from the Document Gallery.</p>
<p>There are hundreds of Maple Learn documents in the Document Gallery, available <a href="http://learn.maplesoft.com/examples">here</a>. Instead of writing Maple Learn documents from scratch, I like to search the gallery for documents relating to my topic. I then select a document, and just modify it slightly to get what I want.</p>
<p><strong>2. Toggling from Math Mode to Text Mode</strong></p>
<p>If you want to write text in a group element, it’s best to toggle to text mode (otherwise Maple Learn will treat your text as math).</p>
<p>While this can be done using the toolbar, there is a nifty keyboard shortcut to toggle to text mode: place your cursor at the beginning of the group element, and press the space key.</p>
<p><img src="/view.aspx?sf=216582_post/image1a.png"></p>
<p><strong>3. Using Double Arrows in Plots to Show Distance</strong></p>
<p>Here’s one for the advanced users. The <a href="https://learn.maplesoft.com/doc/vector-command-rsfwz1xwdl">Vector Command</a> lets you draw arrows on a Maple Learn plot. Combine two such arrows of the same colour going in opposite directions, and you get a double arrow (see below), which I like to use to represent distances in my Maple Learn documents.</p>
<p><img src="/view.aspx?sf=216582_post/image2.png">Indeed, <a href="https://learn.maplesoft.com/doc/product-rule-visualization-jny5z44vf0">here</a> is an example document where I use double arrows to provide a visualization of the product rule in calculus (plot pictured below). Notice how the double arrows (created using the vector command) represent distances in the plot.</p>
<p><img src="/view.aspx?sf=216582_post/image3a.png"></p>
<p>Comment your favourite tips and tricks down below!</p>
<p>I’m looking for users’ favourite tips and tricks in <a href="http://learn.maplesoft.com">Maple Learn</a>. Specifically, small pieces of advice that most people don’t know about, but that helped you create better Maple Learn documents. For instance,</p>
<ul>
<li style="margin-left: 36pt;">A favorite feature that you think is hard to discover;</li>
<li style="margin-left: 36pt;">Common techniques you use when creating documents;</li>
<li style="margin-left: 36pt;">Things about Maple Learn you wish you knew when you started.</li>
</ul>
<p>These tricks could be for newbies or for experienced users.</p>
<p>To start off the discussion, let me share three of my own favorite tricks in Maple Learn.</p>
<p><strong>1. Using Documents from the Document Gallery</strong></p>
<p>Writing a Maple Learn document from scratch can seem overwhelming, especially for beginners. A much easier way to create documents is to start with a template from the Document Gallery.</p>
<p>There are hundreds of Maple Learn documents in the Document Gallery, available <a href="http://learn.maplesoft.com/examples">here</a>. Instead of writing Maple Learn documents from scratch, I like to search the gallery for documents relating to my topic. I then select a document, and just modify it slightly to get what I want.</p>
<p><strong>2. Toggling from Math Mode to Text Mode</strong></p>
<p>If you want to write text in a group element, it’s best to toggle to text mode (otherwise Maple Learn will treat your text as math).</p>
<p>While this can be done using the toolbar, there is a nifty keyboard shortcut to toggle to text mode: place your cursor at the beginning of the group element, and press the space key.</p>
<p><img src="/view.aspx?sf=216582_post/image1a.png"></p>
<p><strong>3. Using Double Arrows in Plots to Show Distance</strong></p>
<p>Here’s one for the advanced users. The <a href="https://learn.maplesoft.com/doc/vector-command-rsfwz1xwdl">Vector Command</a> lets you draw arrows on a Maple Learn plot. Combine two such arrows of the same colour going in opposite directions, and you get a double arrow (see below), which I like to use to represent distances in my Maple Learn documents.</p>
<p><img src="/view.aspx?sf=216582_post/image2.png">Indeed, <a href="https://learn.maplesoft.com/doc/product-rule-visualization-jny5z44vf0">here</a> is an example document where I use double arrows to provide a visualization of the product rule in calculus (plot pictured below). Notice how the double arrows (created using the vector command) represent distances in the plot.</p>
<p><img src="/view.aspx?sf=216582_post/image3a.png"></p>
<p>Comment your favourite tips and tricks down below!</p>
216582Wed, 19 Jan 2022 14:33:38 ZpstaadeckerpstaadeckerRandom Sample from Data Set
https://www.mapleprimes.com/posts/216566-Random-Sample-From-Data-Set?ref=Feed:MaplePrimes:New Posts
<p>A user would like to know if it is possible to specify a data set say, x:=[1,2,3,4,5,6] and then extract a random sample from that data set, i.e. xsample:=[3,2,4] for a bootstrapping-type calculation.</p>
<p>We suggested they use something like the following:</p>
<form name="worksheet_form">
<table align="center" width="768">
<tbody>
<tr>
<td>
<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="restart; with(Statistics); my_data := [1, 2, 4, 5.5, 5.5, 6]; X := RandomVariable(EmpiricalDistribution(my_data)); s := Sample(X, 10); Bootstrap(Mean, X, samplesize = 4, replications = 10000)" height="201" src="/view.aspx?sf=216566_post/175b0f3bb6f70d55f0c260650ae89a0b.gif" style="vertical-align:-184px" width="768"></p>
<table>
<tbody>
<tr valign="baseline">
<td>
<p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="HFloat(3.9984625)" height="23" src="/view.aspx?sf=216566_post/030a8ea1998cd3c690a2ab46b44d7cc1.gif" style="vertical-align:-6px" width="122"></p>
</td>
<td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(1)</td>
</tr>
</tbody>
</table>
<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="NULL" height="23" src="/view.aspx?sf=216566_post/641feb200e74299041e6cce18506cc54.gif" style="vertical-align:-6px" width="9"></p>
</td>
</tr>
</tbody>
</table>
</form>
<p><a href="/view.aspx?sf=216566_post/array-random-sample.mw">Download array-random-sample.mw</a></p>
<p>A user would like to know if it is possible to specify a data set say, x:=[1,2,3,4,5,6] and then extract a random sample from that data set, i.e. xsample:=[3,2,4] for a bootstrapping-type calculation.</p>
<p>We suggested they use something like the following:</p>
<form name="worksheet_form">
<table align="center" width="768">
<tbody>
<tr>
<td>
<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="restart; with(Statistics); my_data := [1, 2, 4, 5.5, 5.5, 6]; X := RandomVariable(EmpiricalDistribution(my_data)); s := Sample(X, 10); Bootstrap(Mean, X, samplesize = 4, replications = 10000)" height="201" src="/view.aspx?sf=216566_post/175b0f3bb6f70d55f0c260650ae89a0b.gif" style="vertical-align:-184px" width="768"></p>
<table>
<tbody>
<tr valign="baseline">
<td>
<p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="HFloat(3.9984625)" height="23" src="/view.aspx?sf=216566_post/030a8ea1998cd3c690a2ab46b44d7cc1.gif" style="vertical-align:-6px" width="122"></p>
</td>
<td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(1)</td>
</tr>
</tbody>
</table>
<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="NULL" height="23" src="/view.aspx?sf=216566_post/641feb200e74299041e6cce18506cc54.gif" style="vertical-align:-6px" width="9"></p>
</td>
</tr>
</tbody>
</table>
</form>
<p><a href="/view.aspx?sf=216566_post/array-random-sample.mw">Download array-random-sample.mw</a></p>
216566Mon, 17 Jan 2022 20:57:13 ZTechnicalSupportTechnicalSupportBohemian Matrix Calendar 2022 is up!
https://www.mapleprimes.com/posts/216551-Bohemian-Matrix-Calendar-2022-Is-Up?ref=Feed:MaplePrimes:New Posts
<p> </p>
<p>The Bohemian Matrix Calendar 2022 is up! You may find it at <a href="https://rcorless.github.io/">https://rcorless.github.io/</a> (four versions: letter/A4 paper, Sunday/Monday start to the week).</p>
<p>It prints quite well (with proper equipment). I wish you all the best for 2022.</p>
<p> </p>
<p><img height="100px" src="/view.aspx?sf=216551_post/UHTZD511nrow3258.png" width="100px"></p>
<p> </p>
<p>The Bohemian Matrix Calendar 2022 is up! You may find it at <a href="https://rcorless.github.io/">https://rcorless.github.io/</a> (four versions: letter/A4 paper, Sunday/Monday start to the week).</p>
<p>It prints quite well (with proper equipment). I wish you all the best for 2022.</p>
<p> </p>
<p><img height="100px" src="/view.aspx?sf=216551_post/UHTZD511nrow3258.png" width="100px"></p>
216551Fri, 14 Jan 2022 17:21:16 ZrcorlessrcorlessOnline Tutoring with Maple Learn
https://www.mapleprimes.com/maplesoftblog/216549-Online-Tutoring-With-Maple-Learn?ref=Feed:MaplePrimes:New Posts
<p>Since the start of the pandemic, I have been involved in online mathematics tutoring. I tried many different applications to best communicate with my students, and ended up sticking with Maple Learn. Here’s my setup, and why I chose Maple Learn.</p>
<p><strong>My Setup</strong></p>
<p>When I have an online tutoring session, I join a scheduled video call to “see” my students. I then open a blank Maple Learn document, and share my screen. I explain whatever I need to explain, while writing key information on the Maple Learn document. When I don’t want Learn to interpret what I write, I go into text mode; when I do (e.g. when I want to graph a function), I stay in math mode. When the class is over, I send the document’s sharelink to my students by email, so that they can access it. </p>
<p><a href="https://learn.maplesoft.com/?d=EQFLDJLFPFHUEOMQFOJHBRHFJTLUKLPKANJPNHCKAHPTITNMDNALETNJLNKHKHIUKLPNCLMPDTPKCODHAJIMEKJKFPEPFSGTNPMQ">Here</a> is an example of a Maple Learn document (pictured below) that I created while teaching trigonometry to a student. Keep in mind that I typed this while on call with the student, so the document is very simple - it only uses the most basic features of Maple Learn.</p>
<p><img src="/view.aspx?sf=216549_post/Screen_Shot_2022-01-14_at_8.56.33_AM_copy.png"></p>
<p> </p>
<p><strong>Why I Chose Maple Learn</strong></p>
<p>My main student wants me to teach him trigonometry ahead of it being taught to him at school. For this, I need to be able to write lots of text and math easily, while on video call with him. </p>
<p>Microsoft Word is not good enough for this: the equation editor is too clumsy. I also tried drawing tools where you can move your mouse to draw on the screen, but they make it too hard to write text. I even tried pointing a camera at my desk and writing the notes by hand, but my handwriting is terrible, and I could never find the right position for the camera. That’s the main reason why I chose Maple Learn: it lets me write both text and math quickly and simply, unlike many other applications.</p>
<p>There are some other benefits to using Maple Learn. I like that I can organize what I write in a visually appealing manner on the canvas, by moving groups around. I like that I can graph functions within Maple Learn, without having to open a graphing calculator in a separate tab. Finally, I find the sharelink feature convenient for sending the notes to my students after class.</p>
<p>Disclaimer: I discovered Maple Learn while working at Maplesoft during a co-op term.</p>
<p dir="ltr">Since the start of the pandemic, I have been involved in online mathematics tutoring. I tried many different applications to best communicate with my students, and ended up sticking with Maple Learn. Here’s my setup, and why I chose Maple Learn.</p>
<p dir="ltr"><strong>My Setup</strong></p>
<p dir="ltr">When I have an online tutoring session, I join a scheduled video call to “see” my students. I then open a blank Maple Learn document, and share my screen. I explain whatever I need to explain, while writing key information on the Maple Learn document. When I don’t want Learn to interpret what I write, I go into text mode; when I do (e.g. when I want to graph a function), I stay in math mode. When the class is over, I send the document’s sharelink to my students by email, so that they can access it. </p>
<p dir="ltr"><a href="https://learn.maplesoft.com/?d=EQFLDJLFPFHUEOMQFOJHBRHFJTLUKLPKANJPNHCKAHPTITNMDNALETNJLNKHKHIUKLPNCLMPDTPKCODHAJIMEKJKFPEPFSGTNPMQ">Here</a> is an example of a Maple Learn document (pictured below) that I created while teaching trigonometry to a student. Keep in mind that I typed this while on call with the student, so the document is very simple - it only uses the most basic features of Maple Learn.</p>
<p dir="ltr"><img src="/view.aspx?sf=216549_post/Screen_Shot_2022-01-14_at_8.56.33_AM_copy.png"></p>
<p dir="ltr"> </p>
<p dir="ltr"><strong>Why I Chose Maple Learn</strong></p>
<p dir="ltr">My main student wants me to teach him trigonometry ahead of it being taught to him at school. For this, I need to be able to write lots of text and math easily, while on video call with him. </p>
<p dir="ltr">Microsoft Word is not good enough for this: the equation editor is too clumsy. I also tried drawing tools where you can move your mouse to draw on the screen, but they make it too hard to write text. I even tried pointing a camera at my desk and writing the notes by hand, but my handwriting is terrible, and I could never find the right position for the camera. That’s the main reason why I chose Maple Learn: it lets me write both text and math quickly and simply, unlike many other applications.</p>
<p dir="ltr">There are some other benefits to using Maple Learn. I like that I can organize what I write in a visually appealing manner on the canvas, by moving groups around. I like that I can graph functions within Maple Learn, without having to open a graphing calculator in a separate tab. Finally, I find the sharelink feature convenient for sending the notes to my students after class.</p>
<p>Disclaimer: I discovered Maple Learn while working at Maplesoft during a co-op term.</p>
216549Fri, 14 Jan 2022 14:03:23 ZpstaadeckerpstaadeckerSphere as a projection from 5d to 3d.
https://www.mapleprimes.com/posts/216526-Sphere-As-A-Projection-From-5d-To-3d?ref=Feed:MaplePrimes:New Posts
<p>As always, it's just about drawings.<br>
The parametric equation of a circle has 3 variables and two equations. In 3-dimensional space, a circle is a spiral, but we only need one projection of this spiral into 2-dimensional space, and we also know how the rest 2 it's projections on flat space look.<br>
If we look at the equation of the sphere in parametric form, we will see that these are 3 equations and 5 variables:<br>
x1 = sin(x4)*cos(x5); <br>
x2 = sin(x4)*sin(x5); <br>
x3 = cos(x4);<br>
And so I wanted to see how the remaining 9 projections of the sphere onto 3-dimensional space look. It is very easy to do this with Maple.<br>
<a href="/view.aspx?sf=216526_post/SPHERE.mw">SPHERE.mw</a><br>
<img src="/view.aspx?sf=216526_post/SPHERE_10.gif"><img src="/view.aspx?sf=216526_post/SPHERE_9.gif"><img src="/view.aspx?sf=216526_post/SPHERE_8.gif"><img src="/view.aspx?sf=216526_post/SPHERE_7.gif"><img src="/view.aspx?sf=216526_post/SPHERE_6.gif"><img src="/view.aspx?sf=216526_post/SPHERE_5.gif"><img src="/view.aspx?sf=216526_post/SPHERE_4.gif"><img src="/view.aspx?sf=216526_post/SPHERE_3.gif"><img src="/view.aspx?sf=216526_post/SPHERE_2.gif"><img src="/view.aspx?sf=216526_post/SPHERE_1.gif"></p>
<p>As always, it's just about drawings.<br>
The parametric equation of a circle has 3 variables and two equations. In 3-dimensional space, a circle is a spiral, but we only need one projection of this spiral into 2-dimensional space, and we also know how the rest 2 it's projections on flat space look.<br>
If we look at the equation of the sphere in parametric form, we will see that these are 3 equations and 5 variables:<br>
x1 = sin(x4)*cos(x5); <br>
x2 = sin(x4)*sin(x5); <br>
x3 = cos(x4);<br>
And so I wanted to see how the remaining 9 projections of the sphere onto 3-dimensional space look. It is very easy to do this with Maple.<br>
<a href="/view.aspx?sf=216526_post/SPHERE.mw">SPHERE.mw</a><br>
<img src="/view.aspx?sf=216526_post/SPHERE_10.gif"><img src="/view.aspx?sf=216526_post/SPHERE_9.gif"><img src="/view.aspx?sf=216526_post/SPHERE_8.gif"><img src="/view.aspx?sf=216526_post/SPHERE_7.gif"><img src="/view.aspx?sf=216526_post/SPHERE_6.gif"><img src="/view.aspx?sf=216526_post/SPHERE_5.gif"><img src="/view.aspx?sf=216526_post/SPHERE_4.gif"><img src="/view.aspx?sf=216526_post/SPHERE_3.gif"><img src="/view.aspx?sf=216526_post/SPHERE_2.gif"><img src="/view.aspx?sf=216526_post/SPHERE_1.gif"></p>
216526Wed, 12 Jan 2022 17:38:48 Zone manone man