EV1 and EV2 sageplot 3d interactives

source/linear-algebra/source/01-LE/01.ptx

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

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

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

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

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

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

@@ -0,0 +1,9 @@
+v1 = vector([1,-1,2])
+v2 = vector([1,2,1])
+
+# illustrate set of two vectors
+
+p = plot(v1,thickness=5)
+p += plot(v2,thickness=5)
+p=p.rotate([1,0,0],3*pi/4)
+p

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

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

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

@@ -3,8 +3,8 @@ p = plot([])
 
 # define three vectors
 v1 = vector([1,-1,0])
-v2 = vector(FIXME)
-v3 = vector(FIXME)
+v2 = vector([-2,0,1])
+v3 = vector([-2,-2,2])
 
 # do this 100 times
 for _ in range(100):
@@ -13,9 +13,9 @@ for _ in range(100):
     b = randrange(-9,10)
     c = randrange(-9,10)
     # create linear combination
-    linear_combo = a*v1 + b*v2 + FIXME
+    linear_combo = a*v1 + b*v2 + c*v3
     # add it to the plot
-    p += plot(linear_combo)
+    p += plot(linear_combo,thickness=2)
 
 # show the plot
-show(p)
+p

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

@@ -0,0 +1,59 @@
+<p>
+  Enter several pairs of coefficients <m>(a,b)</m>, separated by commas:
+  <mathInput name="in" minwidth="500" prefill="(1,1),(-2,1),(-1,-2)" />
+</p>
+
+<setup>
+  <math name="v"> (1,2)</math>
+  <math name="w"> (-1,1)</math>
+  <mathList name="l">$in</mathList>
+  <sampleRandomNumbers numSamples="10" from="-6" to="6" name="a" asList="true"/>
+  <sampleRandomNumbers numSamples="10" from="-6" to="6" name="b" asList="true"/>
+</setup>
+
+<triggerSet>
+  <!--<callAction actionName="deleteChildren" target="$g" number="1000"/>-->
+  <callAction actionName="addChildren" target="$g">
+    <vector draggable="false" styleNumber="1" head="$v" />
+    <label anchor="$v" positionFromAnchor="right">
+      <m>\left[\begin{array}{c} $v.x \\ $v.y\end{array}\right]</m>
+    </label>
+    <vector draggable="false" styleNumber="2" head="$w" />
+    <label anchor="$w" positionFromAnchor="left">
+      <m>\left[\begin{array}{c} $w.x \\ $w.y\end{array}\right]</m>
+    </label>
+    <repeat for="$l" valueName="c">
+      <vector draggable="false" styleNumber="3" head="$c.x*$v+$c.y*$w"/>
+    </repeat>
+  </callAction>
+
+    <label>Plot the above linear combinations</label>
+</triggerSet>
+
+<callAction actionName="deleteChildren" target="$g" number="1000"><label>Reset plot</label></callAction>
+
+<triggerSet>
+  <label>Add 10 random linear combinations</label>
+
+  <callAction target="$a" actionName="resample"/>
+  <callAction target="$b" actionName="resample"/>
+  <callAction actionName="addChildren" target="$g">
+    <repeatForSequence from="0" to="10" step="1" valueName="i">
+       <vector draggable="false" styleNumber="4" head="$a[$i]*$v+$b[$i]*$w"/>
+    </repeatForSequence>
+  </callAction>
+</triggerSet>
+
+<graph name="g" xmin="-10" ymin="-10" xmax="10" ymax="10">
+  <description>Graph of two vectors and linear combinations thereof</description>
+
+    <vector draggable="false" styleNumber="1" head="$v" />
+    <label anchor="$v" positionFromAnchor="right">
+      <m>\left[\begin{array}{c} $v.x \\ $v.y\end{array}\right]</m>
+    </label>
+    <vector draggable="false" styleNumber="2" head="$w" />
+    <label anchor="$w" positionFromAnchor="left">
+      <m>\left[\begin{array}{c} $w.x \\ $w.y\end{array}\right]</m>
+    </label> 
+
+</graph>