source: CGBLisp/latex-doc/examples.tex@ 1

Last change on this file since 1 was 1, checked in by Marek Rychlik, 15 years ago

First import of a version circa 1997.
File size: 7.2 KB
Line 
1\begin{verbatim}
2;;----------------------------------------------------------------
3;;
4;; (STRING-GROBNER "[x^2+y,x-y]" '(X Y))
5;;
6;;----------------------------------------------------------------
7Args:[ X^2 + Y, X - Y ]
8[ X - Y, Y^2 + Y ]
9;;----------------------------------------------------------------
10;;
11;; (STRING-GROBNER "[y-x^2,z-x^3]" '(X Y Z) :ORDER #'GREVLEX>)
12;;
13;;----------------------------------------------------------------
14Args:[ - X^2 + Y, - X^3 + Z ]
15[ X^2 - Y, X * Y - Z, Y^2 - X * Z ]
16;;----------------------------------------------------------------
17;;
18;; (STRING-GROBNER-SYSTEM "[u*x+y,x+y]" '(X Y) '(U))
19;;
20;;----------------------------------------------------------------
21------------------- CASE 1 -------------------
22Condition:
23 Green list: [ U ]
24 Red list: [ ]
25 Basis: [ (1) * Y, (1) * X ]
26------------------- CASE 2 -------------------
27Condition:
28 Green list: [ ]
29 Red list: [ U, U - 1 ]
30 Basis: [ (U - 1) * X, ( - U + 1) * Y ]
31------------------- CASE 3 -------------------
32Condition:
33 Green list: [ U - 1 ]
34 Red list: [ U ]
35 Basis: [ (1) * X + (1) * Y ]
36;;----------------------------------------------------------------
37;;
38;; (STRING-GROBNER-SYSTEM "[u*x+y,x+y]" '(X Y) '(U) :COVER '(("[u-1]" "[]")))
39;;
40;;----------------------------------------------------------------
41------------------- CASE 1 -------------------
42Condition:
43 Green list: [ U - 1 ]
44 Red list: [ U ]
45 Basis: [ (1) * X + (1) * Y ]
46;;----------------------------------------------------------------
47;;
48;; (STRING-READ-POLY "[x^3+3*x^2+3*x+1]" '(X))
49;;
50;;----------------------------------------------------------------
51Args:[ X^3 + 3 * X^2 + 3 * X + 1 ]
52[ RETURN VALUE 1]-->> ([ (((3) . 1) ((2) . 3) ((1) . 3) ((0) . 1)))
53
54;;----------------------------------------------------------------
55;;
56;; (STRING-ELIMINATION-IDEAL "[x^2+y^2-2,x*y-1]" '(X Y) 1)
57;;
58;;----------------------------------------------------------------
59Args:[ X^2 + Y^2 - 2, X * Y - 1 ]
60[ Y^4 - 2 * Y^2 + 1 ]
61;;----------------------------------------------------------------
62;;
63;; (STRING-IDEAL-SATURATION-1 "[x^2*y,y^3]" "x" '(X Y))
64;;
65;;----------------------------------------------------------------
66[ Y ]
67;;----------------------------------------------------------------
68;;
69;; (STRING-IDEAL-POLYSATURATION-1 "[x^2*y,y^3]" "[x,y]" '(X Y))
70;;
71;;----------------------------------------------------------------
72Args1:[ X^2 * Y, Y^3 ]
73Args2:[ X, Y ]
74[ 1 ]
75;;----------------------------------------------------------------
76;;
77;; (STRING-COND '("[u^2-v]" "[v-1]") '(U V) #'GREVLEX>)
78;;
79;;----------------------------------------------------------------
80[ RETURN VALUE 1]-->> (((((2 0) . 1) ((0 1) . -1))) ((((0 1) . 1) ((0 0) . -1))))
81
82;;----------------------------------------------------------------
83;;
84;; (STRING-COVER '(("[u^2-v]" "[u]") ("[u+v]" "[]")) '(U V) #'GREVLEX>)
85;;
86;;----------------------------------------------------------------
87[ RETURN VALUE 1]-->> ((((((2 0) . 1) ((0 1) . -1))) ((((1 0) . 1)))) (((((1 0) . 1) ((0 1) . 1))) NIL))
88
89;;----------------------------------------------------------------
90;;
91;; (STRING-DETERMINE "[u*x+y,v*x^2+y^2]" '(X Y) '(U V) :COND '("[u,v]" "[v-1]") :MAIN-ORDER #'LEX>)
92;;
93;;----------------------------------------------------------------
94------------------- CASE 1 -------------------
95Condition:
96 Green list: [ U, V ]
97 Red list: [ V - 1, 1 ]
98 Basis: [ (1) * Y, (1) * Y^2 ]
99;;----------------------------------------------------------------
100;;
101;; (PARSE-STRING-TO-SORTED-ALIST "x^2+y^3" '(X Y) #'GREVLEX>)
102;;
103;;----------------------------------------------------------------
104[ RETURN VALUE 1]-->> (((0 3) . 1) ((2 0) . 1))
105
106;;----------------------------------------------------------------
107;;
108;; (PARSE-STRING-TO-SORTED-ALIST "[x^2+y^3,x-y]" '(X Y) #'GREVLEX>)
109;;
110;;----------------------------------------------------------------
111[ RETURN VALUE 1]-->> ([ (((0 3) . 1) ((2 0) . 1)) (((1 0) . 1) ((0 1) . -1)))
112
113;;----------------------------------------------------------------
114;;
115;; (TRANSLATE-STATEMENTS (COLLINEAR A B C) (PERPENDICULAR A B A C))
116;;
117;;----------------------------------------------------------------
118[ RETURN VALUE 1]-->> ((((+ (- (* B1 C2) (* B2 C1)) (- (* A2 C1) (* A1 C2)) (- (* A1 B2) (* A2 B1))))
119 ((+ (* (- A1 B1) (- A1 C1)) (* (- A2 B2) (- A2 C2)))))
120 (B1 B2 A1 A2 C1 C2))
121
122;;----------------------------------------------------------------
123;;
124;; (TRANSLATE-THEOREM ((PERPENDICULAR A B C D) (PERPENDICULAR C D E F))
125 ((PARALLEL A B E F) (IDENTICAL-POINTS C D)))
126;;
127;;----------------------------------------------------------------
128[ RETURN VALUE 1]-->> (((+ (* (- A1 B1) (- C1 D1)) (* (- A2 B2) (- C2 D2)))
129 (+ (* (- C1 D1) (- E1 F1)) (* (- C2 D2) (- E2 F2))))
130 (A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 F1 F2))
131[ RETURN VALUE 2]-->> ((((- (* (- A1 B1) (- E2 F2)) (* (- A2 B2) (- E1 F1)))) ((- C1 D1) (- C2 D2)))
132 (A1 A2 B1 B2 E1 E2 F1 F2 C1 C2 D1 D2))
133
134;;----------------------------------------------------------------
135;;
136;; (TRANSLATE-THEOREM ((PERPENDICULAR A B A C) (MIDPOINT B C M) (MIDPOINT A M O) (COLLINEAR B H C)
137 (PERPENDICULAR A H B C))
138 ((EQUIDISTANT M O H O) (IDENTICAL-POINTS B C)))
139;;
140;;----------------------------------------------------------------
141[ RETURN VALUE 1]-->> (((+ (* (- A1 B1) (- A1 C1)) (* (- A2 B2) (- A2 C2))) (- (* 2 M1) B1 C1)
142 (- (* 2 M2) B2 C2) (- (* 2 O1) A1 M1) (- (* 2 O2) A2 M2)
143 (+ (- (* H1 C2) (* H2 C1)) (- (* B2 C1) (* B1 C2)) (- (* B1 H2) (* B2 H1)))
144 (+ (* (- A1 H1) (- B1 C1)) (* (- A2 H2) (- B2 C2))))
145 (M1 M2 O1 O2 A1 A2 H1 H2 B1 B2 C1 C2))
146[ RETURN VALUE 2]-->> ((((- (+ (EXPT (- M1 O1) 2) (EXPT (- M2 O2) 2))
147 (+ (EXPT (- H1 O1) 2) (EXPT (- H2 O2) 2))))
148 ((- B1 C1) (- B2 C2)))
149 (M1 M2 H1 H2 O1 O2 B1 B2 C1 C2))
150
151;;----------------------------------------------------------------
152;;
153;; (PROVE-THEOREM ((PERPENDICULAR A B C D) (PERPENDICULAR C D E F)) ((PARALLEL A B E F) (IDENTICAL-POINTS C D)))
154;;
155;;----------------------------------------------------------------
156[ 1 ]
157;;----------------------------------------------------------------
158;;
159;; (PROVE-THEOREM ((PERPENDICULAR A B A C) (MIDPOINT B C M) (MIDPOINT A M O) (COLLINEAR B H C)
160 (PERPENDICULAR A H B C))
161 ((EQUIDISTANT M O H O) (IDENTICAL-POINTS B C)))
162;;
163;;----------------------------------------------------------------
164[ 1 ]
165;;----------------------------------------------------------------
166;;
167;; (PROVE-THEOREM ((PERPENDICULAR A B A C) (IDENTICAL-POINTS B C))
168 ((IDENTICAL-POINTS A B) (IDENTICAL-POINTS A C)))
169;;
170;;----------------------------------------------------------------
171[ B1 - C1, B2 - C2, A1^2 + A2^2 - 2 * A1 * C1 + C1^2 - 2 * A2 * C2 + C2^2 ]
172;;----------------------------------------------------------------
173;;
174;; (PROVE-THEOREM ((PERPENDICULAR A B A C) (IDENTICAL-POINTS B C))
175 ((IDENTICAL-POINTS A B) (REAL-IDENTICAL-POINTS A C)))
176;;
177;;----------------------------------------------------------------
178[ 1 ]
179\end{verbatim}
Note: See TracBrowser for help on using the repository browser.