add calculations for false properties to AT5

Author: StevenClontz

source/linear-algebra/exercises/outcomes/AT/AT5/generator.sage

@@ -15,7 +15,7 @@ class Generator(BaseGenerator):
 
         def verify(plus,times,hardfalseproperties=[]):
             trueproperties={}
-            falseproperties=hardfalseproperties
+            falseproperties={}
             for prop in true_property_options:
                     if prop == "add_assoc":
                         LHS = plus(v1,plus(v2,v3))
@@ -38,9 +38,9 @@ class Generator(BaseGenerator):
                     LHS = vectorsimplify(LHS)
                     RHS = vectorsimplify(RHS)
                     if LHS == RHS:
-                        trueproperties[prop]=vectorsimplify(LHS)
+                        trueproperties[prop]=LHS
                     else:
-                        falseproperties.append(prop)
+                        falseproperties[prop]={"LHS": LHS, "RHS": RHS}
             for prop in false_only_property_options:
                 if "dist_s" in trueproperties and "mul_id" in trueproperties:
                     if prop == "add_id":
@@ -145,5 +145,5 @@ class Generator(BaseGenerator):
             "trueproperty": {
                 trueproperty: verification
             },
-            "falseproperties": {f: True for f in falseproperties},
+            "falseproperties": falseproperties,
         }

source/linear-algebra/exercises/outcomes/AT/AT5/template.xml

@@ -47,30 +47,6 @@ Show both sides simplify to <m>{{add_comm}}</m>.
         </outtro>
     </knowl>
     <!-- {{/add_comm}} -->
-    <!-- {{#add_id}} -->
-    <!-- <knowl>
-        <content>
-            <p>
-Show that there exists an additive identity element, that is:
-                <me>
-\text{There exists }(w,z)\in V
-\text{ such that }(x,y)\oplus(w,z)=(x,y).
-                </me>
-            </p>
-        </content>
-        <outtro><p>TODO</p></outtro>
-    </knowl> -->
-    <!-- {{/add_id}} -->
-    <!-- {{#add_inv}} -->
-    <!-- <knowl>
-        <content>
-            <p>
-Show that additive inverses exist.
-            </p>
-        </content>
-        <outtro><p>TODO</p></outtro>
-    </knowl> -->
-    <!-- {{/add_inv}} -->
     <!-- {{#mul_assoc}} -->
     <knowl>
         <content>
@@ -160,14 +136,16 @@ any one of the following properties does not hold:
                 <!-- {{#add_assoc}} -->
                 <item>
                     <p>
-Vector addition is not associative.
+Vector addition is not associative: <me>(x_1,y_1)\oplus((x_2,y_2)\oplus(x_3,y_3))={{LHS}}</me>
+<me>((x_1,y_1)\oplus(x_2,y_2))\oplus(x_3,y_3)={{RHS}}</me>
                     </p>
                 </item>
                 <!-- {{/add_assoc}} -->
                 <!-- {{#add_comm}} -->
                 <item>
                     <p>
-Vector addition is not commutative.
+Vector addition is not commutative: <me>(x_1,y_1)\oplus(x_2,y_2)={{LHS}}</me>
+<me>(x_2,y_2)\oplus(x_1,y_1)={{RHS}}</me>
                     </p>
                 </item>
                 <!-- {{/add_comm}} -->
@@ -188,28 +166,33 @@ Additive inverses do not always exist.
                 <!-- {{#mul_assoc}} -->
                 <item>
                     <p>
-Scalar multiplication is not associative.
+Scalar multiplication is not associative: <me>c\odot(d\odot(x,y))={{LHS}}</me>
+<me>(cd)\odot(x,y)={{RHS}}</me>
                     </p>
                 </item>
                 <!-- {{/mul_assoc}} -->
                 <!-- {{#mul_id}} -->
                 <item>
                     <p>
-<m>1</m> is not a scalar multiplication identity.
+<m>1</m> is not a scalar multiplication identity: <me>1\odot(x,y)={{LHS}} \neq (x,y)</me>
                     </p>
                 </item>
                 <!-- {{/mul_id}} -->
                 <!-- {{#dist_v}} -->
                 <item>
                     <p>
-Scalar multiplication does not distribute over vector addition.
+Scalar multiplication does not distribute over vector addition:
+<me>c\odot((x_1,y_1)\oplus(x_2,y_2))={{LHS}}</me>
+<me>(c\odot(x_1,y_1))\oplus(c\odot(x_2,y_2))={{RHS}}</me>
                     </p>
                 </item>
                 <!-- {{/dist_v}} -->
                 <!-- {{#dist_s}} -->
                 <item>
                     <p>
-Scalar multiplication does not distribute over scalar addition.
+Scalar multiplication does not distribute over scalar addition:
+<me>(c+d)\odot(x,y)={{LHS}}</me>
+<me>(c\odot(x,y))\oplus(d\odot(x,y))={{RHS}}</me>
                     </p>
                 </item>
                 <!-- {{/dist_s}} -->