Add technology exploration in AT2 (#943)

* Add technology exploration in AT2

* fix bug in linear combo helper

* update AT2 checkit

Author: StevenClontz

source/common/sagemath/library.sage

@@ -578,12 +578,12 @@ class TBIL:
 
     #Vector equation class
     class LinearCombinationFromMatrix(LinearCombination):
-        def __init__(self,A,vars=None):
+        def __init__(self,A,coefficients=None):
             A=A.subdivision(0,0)  # ignores augmented matrices
-            if vars is None:
+            if coefficients is None:
                 self.coefficients=[var(f"x_{i}") for i in range(1,len(A.columns())+1)]
             else:
-                self.coefficients=[vars[:len(A.columns())]]
+                self.coefficients=coefficients[:len(A.columns())]
             self.vectors=[column_matrix(v) for v in A.columns()]
             self.length=min(len(self.coefficients),len(self.vectors))
             self.parentheses=False

source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage

@@ -39,6 +39,7 @@ class Generator(BaseGenerator):
             "Tcols": Tcolumns,
             "Tstandardmatrix": B,
             "vector": v,
-            "Tvector": B*v
+            "Tvector": B*v,
+            "Tcombo": TBIL.LinearCombinationFromMatrix(B,coefficients=list(v))
         }
 

source/linear-algebra/exercises/outcomes/AT/AT2/template.xml

@@ -2,27 +2,43 @@
 <knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
     <knowl>
         <content>
-            <p>Explain and demonstrate how to compute
-                the standard matrix for the linear transformation
-                <m>S:\mathbb{R}^{{Scols}} \to \mathbb{R}^{{Srows}}</m> given by
-                <me>S\left( {{varvector}} \right) = {{varmap}}</me>
-                by computing transformations of the standard basic vectors.</p>
+            <p>
+Explain and demonstrate how to compute
+the standard matrix for the linear transformation
+<m>S:\mathbb{R}^{{Scols}} \to \mathbb{R}^{{Srows}}</m> given by
+<me>S\left( {{varvector}} \right) = {{varmap}}</me>
+by computing transformations of the standard basic vectors.
+            </p>
         </content>
         <outtro>
             <p><me>{{Sstandardmatrix}}</me></p>
         </outtro>
     </knowl>
     <knowl>
         <content>
-            <p>Let <m>T:\mathbb{R}^{{Tcols}} \to \mathbb{R}^{{Trows}}</m>
-              be the linear transformation given by the standard matrix
-              <me>{{Tstandardmatrix}}.</me>
-              Explain and demonstrate how to compute
-              <m>T\left({{vector}}\right)</m> by using the values of
-              transformed standard basic vectors.</p>
+            <p>
+Let <m>T:\mathbb{R}^{{Tcols}} \to \mathbb{R}^{{Trows}}</m>
+be the linear transformation given by the standard matrix
+<me>{{Tstandardmatrix}}.</me>
+Compute <m>T\left({{vector}}\right)</m> using technology.
+            </p>
         </content>
         <outtro>
             <p><me>T\left({{vector}}\right)={{Tvector}}</me></p>
         </outtro>
     </knowl>
+    <knowl>
+        <content>
+            <p>
+Now explain and demonstrate how to compute
+<m>T\left({{vector}}\right)</m> by using the values of
+transformed standard basic vectors.
+            </p>
+        </content>
+        <outtro>
+            <p><me>
+T\left({{vector}}\right)={{Tcombo}}={{Tvector}}
+            </me></p>
+        </outtro>
+    </knowl>
 </knowl>