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EV1 and EV2 sageplot 3d interactives (#1035)
* EV1 plot * Merge branch to fix xml:id error * EV2 interactive * Tweak
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‎source/linear-algebra/source/01-LE/01.ptx‎

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@@ -508,15 +508,15 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>inconsistent linear s
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<figure xml:id="figure-intersecting-planes-one">
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<caption>Intersection of three planes at one point</caption>
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<image xml:id="LE1-image-intersection-planes-one" width="50%" component="print">
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<image xml:id="LE1-image-intersection-planes-one-print" width="50%" component="print">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./sage/LE1-image-intersection-planes-one.sage" parse="text"/>
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</sageplot>
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<description>
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<p>Three planes are shown to intersect at a single point. An arrow points to the point of intersection at coordinates <m>(1,2,3)</m>.</p>
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</description>
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</image>
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<image xml:id="LE1-image-intersection-planes-one" component="html">
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<image xml:id="LE1-image-intersection-planes-one-html" component="html">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./sage/LE1-image-intersection-planes-one.sage" parse="text"/>
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</sageplot>
@@ -528,15 +528,15 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>inconsistent linear s
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<figure xml:id="figure-intersecting-planes-inf">
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<caption>Intersection of three planes at a line</caption>
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<image xml:id="LE1-image-intersection-planes-inf" width="50%" component="print">
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<image xml:id="LE1-image-intersection-planes-inf-print" width="50%" component="print">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./sage/LE1-image-intersection-planes-inf.sage" parse="text"/>
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</sageplot>
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<description>
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<p>Three planes are shown to intersect along a line of points.</p>
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</description>
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</image>
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<image xml:id="LE1-image-intersection-planes-inf" component="html">
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<image xml:id="LE1-image-intersection-planes-inf-html" component="html">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./sage/LE1-image-intersection-planes-inf.sage" parse="text"/>
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</sageplot>
@@ -548,15 +548,15 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>inconsistent linear s
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<figure xml:id="figure-intersecting-planes-zero">
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<caption>Three non-mutually-intersecting planes</caption>
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<image xml:id="LE1-image-intersection-planes-zero" width="50%" component="print">
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<image xml:id="LE1-image-intersection-planes-zero-print" width="50%" component="print">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./sage/LE1-image-intersection-planes-zero.sage" parse="text"/>
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</sageplot>
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<description>
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<p>Three planes are shown to intersect at no common point, although each pair of planes intersects along a line of points.</p>
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</description>
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</image>
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<image xml:id="LE1-image-intersection-planes-zero" component="html">
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<image xml:id="LE1-image-intersection-planes-zero-html" component="html">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./sage/LE1-image-intersection-planes-zero.sage" parse="text"/>
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</sageplot>

‎source/linear-algebra/source/02-EV/01.ptx‎

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@@ -221,27 +221,26 @@ we refer to this real number as a <term>scalar</term>.
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</p>
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</task>
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<task>
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<p component="html">
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Correct the SageMath code cell below to generate
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an illustration of several vectors belonging to
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<me>\vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right],
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\left[\begin{array}{c}-1\\1\end{array}\right]\right\}=
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\setBuilder{a\left[\begin{array}{c}1\\2\end{array}\right]+
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b\left[\begin{array}{c}-1\\1\end{array}\right]}{a, b \in \IR}</me>
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in the <m>xy</m> plane.
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</p>
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<sage component="html">
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<input>
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<xi:include href="./code/ev1-planar-span.sage" parse="text" />
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</input>
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</sage>
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<p component="html">
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Based on this illustration, which of these geometrical objects
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best describes the span of these two vectors?
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<p>
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In addition to the combinations above, use the interactive below to graph an additional
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5 or more vectors belonging to
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<me>\vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right],
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\left[\begin{array}{c}-1\\1\end{array}\right]\right\}=
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\setBuilder{a\left[\begin{array}{c}1\\2\end{array}\right]+
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b\left[\begin{array}{c}-1\\1\end{array}\right]}{a, b \in \IR}</me>
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in the <m>xy</m> plane.
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</p>
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<p component="print">
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Which of these geometrical objects
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best describes the span of these two vectors?
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<interactive label="EV1-interactive-span" platform="doenetml" width="100%">
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<slate surface="doenetml">
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<xi:include parse="text" href="doenet/EV1-span-two-vectors.xml"/>
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</slate>
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<description>
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<p>An interactive that graphs linear combinations of the vectors <m>\left[\begin{array}{c}1\\2\end{array}\right]</m> and
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<m> \left[\begin{array}{c}-1\\1\end{array}\right]</m>.</p>
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</description>
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</interactive>
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<p>
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Which of these geometrical objects best describes the span of these two vectors?
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</p>
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<ol marker="A." cols="4">
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<li>A line</li>
@@ -525,15 +524,15 @@ It is important to remember that
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</p>
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<p>
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For example,
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<me>
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<me>S=
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\setList
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{
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\left[\begin{array}{c} 1 \\ -1 \\ 2 \end{array}\right],
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\left[\begin{array}{c} 1 \\ 2 \\ 1 \end{array}\right]
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}
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</me>
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is a set containing exactly two vectors, while
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<me>
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<me>\vspan S =
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\vspan\setList
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{
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\left[\begin{array}{c} 1 \\ -1 \\ 2 \end{array}\right],
@@ -546,15 +545,34 @@ b\left[\begin{array}{c} 1 \\ 2 \\ 1 \end{array}\right]
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a,b\in\IR
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}
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</me>
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is a set containing infinitely-many vectors. </p>
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<p component="html">See the below
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Sage cell for an illustration.
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</p>
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<sage language="sage" component="html">
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<input>
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<xi:include href="./code/ev1-remark-span.sage" parse="text" />
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</input>
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</sage>
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is a set containing infinitely-many vectors.
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</p>
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<figure>
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<sidebyside widths="45% 45%">
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<image>
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./code/ev1-remark-span1.sage" parse="text" />
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</sageplot>
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<description><p>An interactive 3-D plot showing the two vectors in <m>S</m></p></description>
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</image>
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<image>
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./code/ev1-remark-span2.sage" parse="text" />
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</sageplot>
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<description><p>An interactive 3-D plot showing the vectors in <m>\vspan S</m></p></description>
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</image>
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</sidebyside>
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<caption>
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<p component="html">
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Two interactive 3-D plots showing the two vectors in <m>S</m> on the
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left and <m>\vspan S</m> on the right.
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</p>
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<p component="print">
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Two plots showing the two vectors in <m>S</m> on the
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left and <m>\vspan S</m> on the right.
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</p>
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</caption>
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</figure>
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</remark>
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</subsection>

‎source/linear-algebra/source/02-EV/02.ptx‎

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Original file line numberDiff line numberDiff line change
@@ -262,31 +262,21 @@ The vector does not belong to the span.
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</p>
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</answer>
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</task>
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<task component="html">
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<statement>
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<p>
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Fix the SageMath code below to visualize
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</activity>
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<observation>
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<p>We can use technology to visualize
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<m>\vspan\left\{\left[\begin{array}{c}1\\-1\\0\end{array}\right],
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\left[\begin{array}{c}-2\\0\\1\end{array}\right],\left[\begin{array}{c}-2\\-2\\2\end{array}\right]\right\}</m>.
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</p>
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<sage>
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<input>
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</p>
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<image width="70%">
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<sageplot variant="3d" aspect="1.0">
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<xi:include href="./code/ev2-span-visual.sage" parse="text" />
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</input>
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</sage>
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</statement>
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<answer>
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<program language="sage">
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<code>
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v2 = vector([-2,0,1])
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v3 = vector([-2,-2,2])
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# ...
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linear_combo = a*v1 + b*v2 + c*v3
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</code>
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</program>
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</answer>
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</task>
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</activity>
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</sageplot>
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<description><p>An interactive 3-D plot showing the span</p></description>
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</image>
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<p component="html">Rotate the plot to see that the vectors all lie in the same plane.</p>
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<p component="print">Note that the vectors all lie in the same plane.</p>
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</observation>
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<activity>
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<introduction>
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<p>

‎source/linear-algebra/source/02-EV/code/ev1-remark-span1.sage‎

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v1 = vector([1,-1,2])
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v2 = vector([1,2,1])
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# illustrate set of two vectors
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p = plot(v1,thickness=5)
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p += plot(v2,thickness=5)
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p=p.rotate([1,0,0],3*pi/4)
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p

source/linear-algebra/source/02-EV/code/ev1-remark-span.sage renamed to source/linear-algebra/source/02-EV/code/ev1-remark-span2.sage

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@@ -1,17 +1,13 @@
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v1 = vector([1,-1,2])
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v2 = vector([1,2,1])
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# illustrate set of two vectors
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p = plot(v1)
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p += plot(v2)
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show(p)
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# illustrate the *span* that set
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# illustrate the *span*
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p = plot([])
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for _ in range(1000):
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a = randrange(-99,100)
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b = randrange(-99,100)
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p += plot(a*v1+b*v2)
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show(p)
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p += plot(a*v1+b*v2, thickness=15)
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p=p.rotate([1,0,0],3*pi/4)
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p

‎source/linear-algebra/source/02-EV/code/ev2-span-visual.sage‎

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@@ -3,8 +3,8 @@ p = plot([])
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# define three vectors
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v1 = vector([1,-1,0])
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v2 = vector(FIXME)
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v3 = vector(FIXME)
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v2 = vector([-2,0,1])
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v3 = vector([-2,-2,2])
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# do this 100 times
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for _ in range(100):
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b = randrange(-9,10)
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c = randrange(-9,10)
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# create linear combination
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linear_combo = a*v1 + b*v2 + FIXME
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linear_combo = a*v1 + b*v2 + c*v3
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# add it to the plot
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p += plot(linear_combo)
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p += plot(linear_combo,thickness=2)
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# show the plot
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show(p)
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p

‎source/linear-algebra/source/02-EV/doenet/EV1-span-two-vectors.xml‎

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<p>
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Enter several pairs of coefficients <m>(a,b)</m>, separated by commas:
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<mathInput name="in" minwidth="500" prefill="(1,1),(-2,1),(-1,-2)" />
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</p>
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<setup>
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<math name="v"> (1,2)</math>
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<math name="w"> (-1,1)</math>
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<mathList name="l">$in</mathList>
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<sampleRandomNumbers numSamples="10" from="-6" to="6" name="a" asList="true"/>
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<sampleRandomNumbers numSamples="10" from="-6" to="6" name="b" asList="true"/>
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</setup>
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<triggerSet>
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<!--<callAction actionName="deleteChildren" target="$g" number="1000"/>-->
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<callAction actionName="addChildren" target="$g">
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<vector draggable="false" styleNumber="1" head="$v" />
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<label anchor="$v" positionFromAnchor="right">
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<m>\left[\begin{array}{c} $v.x \\ $v.y\end{array}\right]</m>
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</label>
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<vector draggable="false" styleNumber="2" head="$w" />
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<label anchor="$w" positionFromAnchor="left">
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<m>\left[\begin{array}{c} $w.x \\ $w.y\end{array}\right]</m>
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</label>
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<repeat for="$l" valueName="c">
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<vector draggable="false" styleNumber="3" head="$c.x*$v+$c.y*$w"/>
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</repeat>
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</callAction>
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<label>Plot the above linear combinations</label>
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</triggerSet>
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<callAction actionName="deleteChildren" target="$g" number="1000"><label>Reset plot</label></callAction>
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<triggerSet>
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<label>Add 10 random linear combinations</label>
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<callAction target="$a" actionName="resample"/>
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<callAction target="$b" actionName="resample"/>
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<callAction actionName="addChildren" target="$g">
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<repeatForSequence from="0" to="10" step="1" valueName="i">
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<vector draggable="false" styleNumber="4" head="$a[$i]*$v+$b[$i]*$w"/>
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</repeatForSequence>
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</callAction>
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</triggerSet>
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<graph name="g" xmin="-10" ymin="-10" xmax="10" ymax="10">
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<description>Graph of two vectors and linear combinations thereof</description>
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<vector draggable="false" styleNumber="1" head="$v" />
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<label anchor="$v" positionFromAnchor="right">
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<m>\left[\begin{array}{c} $v.x \\ $v.y\end{array}\right]</m>
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</label>
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<vector draggable="false" styleNumber="2" head="$w" />
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<label anchor="$w" positionFromAnchor="left">
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<m>\left[\begin{array}{c} $w.x \\ $w.y\end{array}\right]</m>
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</label>
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</graph>

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