Fix imaginary artifacts appearing in exponent evaluation.

corywalker · Oct 30, 2018 · c0c521a · c0c521a
1 parent d559b80
commit c0c521a
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Showing 6 changed files with 37 additions and 27 deletions.
diff --git a/expreduce/builtin_list.go b/expreduce/builtin_list.go
@@ -207,10 +207,13 @@ func getListDefinitions() (defs []Definition) {
 			if len(this.GetParts()) >= 3 {
 				mis, isOk := iterspec.MultiSpecFromLists(es, this.GetParts()[2:])
 				if isOk {
-					// Simulate evaluation within Block[]
 					toReturn := atoms.NewExpression([]expreduceapi.Ex{atoms.NewSymbol("System`List")})
 					for mis.Cont() {
-						toReturn.AppendEx(matcher.ReplacePD(this.GetParts()[1].DeepCopy(), es, mis.CurrentPDManager()))
+						thisVal := this.GetParts()[1].DeepCopy()
+						thisVal = matcher.ReplacePD(thisVal, es, mis.CurrentPDManager())
+						thisVal = es.Eval(thisVal)
+						thisVal = matcher.ReplacePD(thisVal, es, mis.CurrentPDManager())
+						toReturn.AppendEx(thisVal)
 						mis.Next()
 					}
 					return toReturn

diff --git a/expreduce/builtin_plot.go b/expreduce/builtin_plot.go
@@ -1,7 +1,6 @@
 package expreduce
 
 func getPlotDefinitions() (defs []Definition) {
-	defs = append(defs, Definition{Name: "ExpreducePlotPoints"})
 	defs = append(defs, Definition{Name: "Plot"})
 	return
 }
diff --git a/expreduce/builtin_power.go b/expreduce/builtin_power.go
@@ -218,6 +218,13 @@ func getPowerDefinitions() (defs []Definition) {
 							inner.DeepCopy(),
 						),
 					)).(*atoms.Flt)
+				// If the exponent has no fractional part, i.e. should be an integer, then we can say there will be no imaginary component to the result.
+				// Reduce[Sin[b*Arg[a]] == 0, b, Reals] // FullSimplify
+				// C[1] \[Element] Integers && a < 0 && (b == 2 C[1] || b == 1 + 2 C[1])
+				if powerFlt.Val.IsInt() {
+					// TODO: We may want to decide this earlier. Figure this out.
+					return re
+				}
 				im :=
 
 					es.Eval(atoms.E(

diff --git a/expreduce/resources.go b/expreduce/resources.go
diff --git a/expreduce/resources/plot.m b/expreduce/resources/plot.m
@@ -1,11 +1,11 @@
 Attributes[ExpreducePlotPoints] = {HoldAll};
-ExpreducePlotPoints[fn_, range_List] := 
+ExpreducePlotPoints[fn_, range_List] :=
   Module[{nPoints, stepSize, replacedFn, unfilteredPoints},
    nPoints = 500;
    stepSize = (range[[3]] - range[[2]])/nPoints // N;
    replacedFn = fn /. range[[1]] -> varOfIteration;
-   unfilteredPoints = 
-    Table[{varOfIteration, replacedFn // N}, {varOfIteration, 
+   unfilteredPoints =
+    Table[{varOfIteration, replacedFn // N}, {varOfIteration,
       range[[2]], range[[3]], stepSize}];
    Select[unfilteredPoints, (Im[#[[2]]] == 0) &]
    ];
@@ -14,23 +14,23 @@
 Attributes[Plot] = {HoldAll, Protected, ReadProtected}
 Plot[fn_, range_List] := Module[{plotPoints, fullRange, displayOptions},
   plotPoints = ExpreducePlotPoints[fn, range];
-  fullRange = {MinMax[Join[plotPoints[[All, 1]], range[[2 ;; 3]]]], 
+  fullRange = {MinMax[Join[plotPoints[[All, 1]], range[[2 ;; 3]]]],
     MinMax[plotPoints[[All, 2]]]};
-  displayOptions = {DisplayFunction -> Identity, 
-    AspectRatio -> GoldenRatio^(-1), Axes -> {True, True}, 
-    AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, 
-    DisplayFunction :> Identity, 
-    Frame -> {{False, False}, {False, False}}, 
-    FrameLabel -> {{None, None}, {None, None}}, 
-    FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
-    GridLines -> {None, None}, 
-    GridLinesStyle -> Directive[GrayLevel[0.5, 0.4]], 
-    Method -> {"DefaultBoundaryStyle" -> Automatic, 
-      "DefaultMeshStyle" -> AbsolutePointSize[6], 
-      "ScalingFunctions" -> None}, PlotRange -> fullRange, 
-    PlotRangeClipping -> True, 
-    PlotRangePadding -> {{Scaled[0.02], Scaled[0.02]}, {Scaled[0.05], 
+  displayOptions = {DisplayFunction -> Identity,
+    AspectRatio -> GoldenRatio^(-1), Axes -> {True, True},
+    AxesLabel -> {None, None}, AxesOrigin -> {0, 0},
+    DisplayFunction :> Identity,
+    Frame -> {{False, False}, {False, False}},
+    FrameLabel -> {{None, None}, {None, None}},
+    FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
+    GridLines -> {None, None},
+    GridLinesStyle -> Directive[GrayLevel[0.5, 0.4]],
+    Method -> {"DefaultBoundaryStyle" -> Automatic,
+      "DefaultMeshStyle" -> AbsolutePointSize[6],
+      "ScalingFunctions" -> None}, PlotRange -> fullRange,
+    PlotRangeClipping -> True,
+    PlotRangePadding -> {{Scaled[0.02], Scaled[0.02]}, {Scaled[0.05],
        Scaled[0.05]}}, Ticks -> {Automatic, Automatic}};
-  Graphics[{{{}, {}, {Directive[Opacity[1.], 
-       RGBColor[0.37, 0.5, 0.71], AbsoluteThickness[1.6]], 
+  Graphics[{{{}, {}, {Directive[Opacity[1.],
+       RGBColor[0.37, 0.5, 0.71], AbsoluteThickness[1.6]],
       Line[plotPoints]}}}, displayOptions]];
diff --git a/expreduce/resources/trig.m b/expreduce/resources/trig.m
@@ -61,6 +61,7 @@
 
 ArcSin[p_Plus] := -ArcSin[-p] /; (MatchQ[p[[1]], -_] || p[[1]] < 0);
 ArcSin[-x_] := -ArcSin[x];
+ArcSin[0] := 0;
 Attributes[ArcSin] = {Listable, NumericFunction, Protected, ReadProtected};
 
 Attributes[ArcCos] = {Listable, NumericFunction, Protected, ReadProtected};