show example calculations for non-properties

Author: StevenClontz

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

@@ -8,6 +8,11 @@ class Generator(BaseGenerator):
         v2 = vector([x2,y2])
         v3 = vector([x3,y3])
         v = vector([x,y])
+        cs, ds, xs, ys = range(2,6)
+        v1s = vector([1,2])
+        v2s = vector([2,3])
+        v3s = vector([3,4])
+        vs = vector([1,2])
         vectorsimplify = lambda v : vector([simplify(expand(x)) for x in v])
 
         true_property_options = ["add_assoc","add_comm","mul_assoc","dist_v","dist_s","mul_id"]
@@ -20,27 +25,44 @@ class Generator(BaseGenerator):
                     if prop == "add_assoc":
                         LHS = plus(v1,plus(v2,v3))
                         RHS = plus(plus(v1,v2),v3)
+                        LHS_sample = plus(v1s,plus(v2s,v3s))
+                        RHS_sample = plus(plus(v1s,v2s),v3s)
                     elif prop == "add_comm":
                         LHS = plus(v1,v2)
                         RHS = plus(v2,v1)
+                        LHS_sample = plus(v1s,v2s)
+                        RHS_sample = plus(v2s,v1s)
                     elif prop == "mul_assoc":
                         LHS = times(c*d,v)
                         RHS = times(c,times(d,v))
+                        LHS_sample = times(cs*ds,vs)
+                        RHS_sample = times(cs,times(ds,vs))
                     elif prop == "mul_id":
                         LHS = times(1,v)
                         RHS = v
+                        LHS_sample = times(1,vs)
+                        RHS_sample = vs
                     elif prop == "dist_v":
                         LHS = times(c,plus(v1,v2))
                         RHS = plus(times(c,v1),times(c,v2))
+                        LHS_sample = times(cs,plus(v1s,v2s))
+                        RHS_sample = plus(times(cs,v1s),times(cs,v2s))
                     elif prop == "dist_s":
                         LHS = times(c+d,v)
                         RHS = plus(times(c,v),times(d,v))
+                        LHS_sample = times(cs+ds,vs)
+                        RHS_sample = plus(times(cs,vs),times(ds,vs))
                     LHS = vectorsimplify(LHS)
                     RHS = vectorsimplify(RHS)
                     if LHS == RHS:
                         trueproperties[prop]=LHS
                     else:
-                        falseproperties[prop]={"LHS": LHS, "RHS": RHS}
+                        falseproperties[prop]={
+                            "LHS": LHS, 
+                            "RHS": RHS, 
+                            "LHS_sample": LHS_sample,
+                            "RHS_sample": RHS_sample
+                        }
             for prop in false_only_property_options:
                 if "dist_s" in trueproperties and "mul_id" in trueproperties:
                     if prop == "add_id":

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

@@ -138,6 +138,8 @@ any one of the following properties does not hold:
                     <p>
 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>
+For example: <me>(1,2)\oplus((2,3)\oplus(3,4))={{LHS_sample}}</me>
+<me>((1,2)\oplus(2,3))\oplus(3,4)={{RHS_sample}}</me>
                     </p>
                 </item>
                 <!-- {{/add_assoc}} -->
@@ -146,6 +148,8 @@ Vector addition is not associative: <me>(x_1,y_1)\oplus((x_2,y_2)\oplus(x_3,y_3)
                     <p>
 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>
+For example: <me>(1,2)\oplus(2,3)={{LHS_sample}}</me>
+<me>(2,3)\oplus(1,2)={{RHS_sample}}</me>
                     </p>
                 </item>
                 <!-- {{/add_comm}} -->
@@ -168,13 +172,16 @@ Additive inverses do not always exist.
                     <p>
 Scalar multiplication is not associative: <me>c\odot(d\odot(x,y))={{LHS}}</me>
 <me>(cd)\odot(x,y)={{RHS}}</me>
+For example: <me>2\odot(3\odot(1,2))={{LHS_sample}}</me>
+<me>(2\cdot 3)\odot(1,2)={{RHS_sample}}</me>
                     </p>
                 </item>
                 <!-- {{/mul_assoc}} -->
                 <!-- {{#mul_id}} -->
                 <item>
                     <p>
 <m>1</m> is not a scalar multiplication identity: <me>1\odot(x,y)={{LHS}} \neq (x,y)</me>
+For example: <me>1\odot(1,2)={{LHS_sample}} \neq (1,2)</me>
                     </p>
                 </item>
                 <!-- {{/mul_id}} -->
@@ -184,6 +191,9 @@ Scalar multiplication is not associative: <me>c\odot(d\odot(x,y))={{LHS}}</me>
 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>
+For example:
+<me>2\odot((1,2)\oplus(2,3))={{LHS_sample}}</me>
+<me>(2\odot(1,2))\oplus(2\odot(2,3))={{RHS_sample}}</me>
                     </p>
                 </item>
                 <!-- {{/dist_v}} -->
@@ -193,6 +203,9 @@ Scalar multiplication does not distribute over vector 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>
+For example:
+<me>(2+3)\odot(1,2)={{LHS_sample}}</me>
+<me>(2\odot(1,2))\oplus(3\odot(1,2))={{RHS_sample}}</me>
                     </p>
                 </item>
                 <!-- {{/dist_s}} -->