@@ -26,22 +26,22 @@ f := Smooth.Softmax( 3 );
2626f := MorphismConstructor( Para, R1 / Para, [ R2, f ] , R3 / Para );
2727# ! ℝ^1 -> ℝ^3 defined by:
2828# !
29- # ! Parameter Object:
29+ # ! Underlying Object:
3030# ! -----------------
3131# ! ℝ^2
3232# !
33- # ! Parametrised Morphism:
34- # ! ----------------------
33+ # ! Underlying Morphism:
34+ # ! -------------------
3535# ! ℝ^3 -> ℝ^3
3636Display( f );
3737# ! ℝ^1 -> ℝ^3 defined by:
3838# !
39- # ! Parameter Object:
39+ # ! Underlying Object:
4040# ! -----------------
4141# ! ℝ^2
4242# !
43- # ! Parametrised Morphism:
44- # ! ----------------------
43+ # ! Underlying Morphism:
44+ # ! -------------------
4545# ! ℝ^3 -> ℝ^3
4646# !
4747# ! ‣ Exp( x1 ) / (Exp( x1 ) + Exp( x2 ) + Exp( x3 ))
@@ -59,22 +59,22 @@ Display( r );
5959g := ReparametriseMorphism( f, r );
6060# ! ℝ^1 -> ℝ^3 defined by:
6161# !
62- # ! Parameter Object:
62+ # ! Underlying Object:
6363# ! -----------------
6464# ! ℝ^2
6565# !
66- # ! Parametrised Morphism:
67- # ! ----------------------
66+ # ! Underlying Morphism:
67+ # ! -------------------
6868# ! ℝ^3 -> ℝ^3
6969Display( g );
7070# ! ℝ^1 -> ℝ^3 defined by:
7171# !
72- # ! Parameter Object:
72+ # ! Underlying Object:
7373# ! -----------------
7474# ! ℝ^2
7575# !
76- # ! Parametrised Morphism:
77- # ! ----------------------
76+ # ! Underlying Morphism:
77+ # ! -------------------
7878# ! ℝ^3 -> ℝ^3
7979# !
8080# ! ‣ Exp( Sqrt( x1 ) ) / (Exp( Sqrt( x1 ) ) + Exp( Cos( x2 ) ) + Exp( x3 ))
@@ -83,32 +83,32 @@ Display( g );
8383l := Para.AffineTransformation( 3 , 2 );
8484# ! ℝ^3 -> ℝ^2 defined by:
8585# !
86- # ! Parameter Object:
86+ # ! Underlying Object:
8787# ! -----------------
8888# ! ℝ^8
8989# !
90- # ! Parametrised Morphism:
91- # ! ----------------------
90+ # ! Underlying Morphism:
91+ # ! -------------------
9292# ! ℝ^11 -> ℝ^2
9393h := PreCompose( g, l );
9494# ! ℝ^1 -> ℝ^2 defined by:
9595# !
96- # ! Parameter Object:
96+ # ! Underlying Object:
9797# ! -----------------
9898# ! ℝ^10
9999# !
100- # ! Parametrised Morphism:
101- # ! ----------------------
100+ # ! Underlying Morphism:
101+ # ! -------------------
102102# ! ℝ^11 -> ℝ^2
103103Display( h );
104104# ! ℝ^1 -> ℝ^2 defined by:
105105# !
106- # ! Parameter Object:
106+ # ! Underlying Object:
107107# ! -----------------
108108# ! ℝ^10
109109# !
110- # ! Parametrised Morphism:
111- # ! ----------------------
110+ # ! Underlying Morphism:
111+ # ! -------------------
112112# ! ℝ^11 -> ℝ^2
113113# !
114114# ! ‣ x1 * (Exp( Sqrt( x9 ) ) / (Exp( Sqrt( x9 ) ) + Exp( Cos( x10 ) ) + Exp( x11 )))
@@ -123,22 +123,22 @@ r := Smooth.Constant( constants );
123123t := ReparametriseMorphism( h, r );
124124# ! ℝ^1 -> ℝ^2 defined by:
125125# !
126- # ! Parameter Object:
126+ # ! Underlying Object:
127127# ! -----------------
128128# ! ℝ^0
129129# !
130- # ! Parametrised Morphism:
131- # ! ----------------------
130+ # ! Underlying Morphism:
131+ # ! -------------------
132132# ! ℝ^1 -> ℝ^2
133133Display( t );
134134# ! ℝ^1 -> ℝ^2 defined by:
135135# !
136- # ! Parameter Object:
136+ # ! Underlying Object:
137137# ! -----------------
138138# ! ℝ^0
139139# !
140- # ! Parametrised Morphism:
141- # ! ----------------------
140+ # ! Underlying Morphism:
141+ # ! -------------------
142142# ! ℝ^1 -> ℝ^2
143143# !
144144# ! ‣ 0.91 * (2.39116 / (5.10727 + Exp( x1 ))) + 0.24 * (2.71611 / (5.10727 + Exp( x1 )))
@@ -148,22 +148,22 @@ Display( t );
148148s := SimplifyMorphism( t, infinity );
149149# ! ℝ^1 -> ℝ^2 defined by:
150150# !
151- # ! Parameter Object:
151+ # ! Underlying Object:
152152# ! -----------------
153153# ! ℝ^0
154154# !
155- # ! Parametrised Morphism:
156- # ! ----------------------
155+ # ! Underlying Morphism:
156+ # ! -------------------
157157# ! ℝ^1 -> ℝ^2
158158Display( s );
159159# ! ℝ^1 -> ℝ^2 defined by:
160160# !
161- # ! Parameter Object:
161+ # ! Underlying Object:
162162# ! -----------------
163163# ! ℝ^0
164164# !
165- # ! Parametrised Morphism:
166- # ! ----------------------
165+ # ! Underlying Morphism:
166+ # ! -------------------
167167# ! ℝ^1 -> ℝ^2
168168# !
169169# ! ‣ (1.47 * Exp( x1 ) + 5.84111) / (Exp( x1 ) + 5.10727)
@@ -175,22 +175,22 @@ ApplyFunctor( iota, Smooth.( 1 ) );
175175psi := ApplyFunctor( iota, Smooth.Sum( 2 ) );
176176# ! ℝ^2 -> ℝ^1 defined by:
177177# !
178- # ! Parameter Object:
178+ # ! Underlying Object:
179179# ! -----------------
180180# ! ℝ^0
181181# !
182- # ! Parametrised Morphism:
183- # ! ----------------------
182+ # ! Underlying Morphism:
183+ # ! -------------------
184184# ! ℝ^2 -> ℝ^1
185185Print( DisplayString( psi ) );
186186# ! ℝ^2 -> ℝ^1 defined by:
187187# !
188- # ! Parameter Object:
188+ # ! Underlying Object:
189189# ! -----------------
190190# ! ℝ^0
191191# !
192- # ! Parametrised Morphism:
193- # ! ----------------------
192+ # ! Underlying Morphism:
193+ # ! -------------------
194194# ! ℝ^2 -> ℝ^1
195195# !
196196# ! ‣ x1 + x2
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