解析几何工具包

hbghlyj

在Mathematica中做解析几何的一个工具包
GeoProver.nb (145.35 KB, 下载次数: 88)

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TSC999

这个包包如何放入程序中以便调用？包包中的东西如何修改、添加和删除？

最好能举个例子说明。

hbghlyj

回复 2# TSC999


    informatik.uni-leipzig.de/~compalg/software/geoprover/
The GeoProver is a small package for mechanized (plane) geometry manipulations with non degeneracy tracing, available for different CAS platforms (Maple, MuPAD, Mathematica, and Reduce).

hbghlyj

TSC999 发表于 2022-4-13 03:53
这个包包如何放入程序中以便调用？包包中的东西如何修改、添加和删除？

最好能举个例子说明。 ...

github.com/hg-graebe/GeoProver
The GeoProver is a small package for mechanized (plane) geometry manipulations with non degeneracy tracing, available for different CAS platforms (Maple, MuPAD, Maxima, Mathematica, and Reduce).

The latest version 1.3 was finished at Jan 20, 2003 and was since that time under casual revision. In particular, in 2017 a version for Maxima was added.

The different packages are build from a common generic source description (macro definitions) and CAS-specific basic inline code together with help system and tests.

After a change of the format of the generic source description this build process has to be fixed.

The precompiled versions for the different target CAS are available in the src directory. See the README.md in the different directories for more details.

hbghlyj

The GeoProver Package for Mechanized (Plane) Geometry Theorem Proving

Basic Data Types

Basic data types are Points, Lines, and Circles.

A point A:=Point(a,b) represents a point with coordinates $(a_1,a_2)$.

A line l:=Line(a,b,c) represents the line $\{ (x,y) : ax+by+c=0 \}$.

A circle c:=Circle(c1,c2,c3,c4) represents the circle $\{ (x,y) : c_1(x^2+y^2)+c_2x+c_3y+c_4=0 \}$.

Available functions

Point(a:Scalar, b:Scalar)	Point constructor. Returns a coding for the point with coordinates (a,b).
altitude(A:Point, B:Point, C:Point)	The altitude from $A$ onto $g(BC)$.
angle_sum(a:Scalar, b:Scalar)	Returns $tan(alpha+beta)$, if $a=tan(alpha),\; b=tan(beta)$.
centroid(A:Point, B:Point, C:Point)	Centroid of the triangle $ABC$.
circle_center(c:Circle)	The center of the circle $c$.
circle_slider(M:Point, A:Point, u:Scalar)	Choose a point on the circle with center $M$ and point $A$ on the perimeter using a rational parametrization with parameter $u$.
circle_sqradius(c:Circle)	The squared radius of the circle $c$.
circumcenter(A:Point, B:Point, C:Point)	The circumcenter of the triangle $ABC$.
csym_point(P:Point, Q:Point)	The point symmetric to $P$ wrt. $Q$ as symmetry center.
eq_angle(A:Point, B:Point, C:Point, D:Point, E:Point, F:Point)	Test for equal angle w(ABC) = w(DEF).
eq_dist(A:Point, B:Point, C:Point, D:Point)	Test for equal distance d(AB) = d(CD).
fixedpoint(A:Point, B:Point, u:Scalar)	The point $D=(1-u)*A+u*B$ on the line AB for a fixed value of u.
intersection_point(a:Line, b:Line)	The intersection point of the lines $a,b$.
is_cc_tangent(c1:Circle, c2:Circle)	Zero iff circles $c\_1$ and $c\_2$ are tangent.
is_cl_tangent(c:Circle, l:Line)	Zero iff the line $l$ is tangent to the circle $c$.
is_collinear(A:Point, B:Point, C:Point)	Zero iff $A,B,C$ are on a common line. For the signed area of the triangle $ABC$ use triangle_area.
is_concurrent(a:Line, b:Line, c:Line)	Zero iff the lines $a,b,c$ pass through a common point.
is_concyclic(A:Point, B:Point, C:Point, D:Point)	Zero iff four given points are on a common circle.
is_equal(A:Scalar, B:Scalar)	Test for equality of A and B.
is_orthogonal(a:Line, b:Line)	zero iff the lines $a,b$ are orthogonal.
is_parallel(a:Line, b:Line)	Zero iff the lines $a,b$ are parallel.
l2_angle(a:Line, b:Line)	Tangens of the angle between $a$ and $b$.
line_slider(a:Line, u:Scalar)	Chooses a point on $a$ using parameter $u$.
median(A:Point, B:Point, C:Point)	The median line from $A$ to $BC$.
midpoint(A:Point, B:Point)	The midpoint of $AB$.
on_bisector(P:Point, A:Point, B:Point, C:Point)	Zero iff $P$ is a point on the (inner or outer) bisector of the angle $\backslash angle\; ABC$.
on_circle(P:Point, c:Circle)	Zero iff $P$ is on the circle $c$.
on_line(P:Point, a:Line)	Zero iff $P$ is on the line $a$.
ortho_line(P:Point, a:Line)	The line through $P$ orthogonal to the line $a$.
orthocenter(A:Point, B:Point, C:Point)	Orthocenter of the triangle $ABC$.
other_cc_point(P:Point, c1:Circle, c2:Circle)	$c\_1$ and $c\_2$ intersect at $P$. The procedure returns the second intersection point.
other_cl_point(P:Point, c:Circle, l:Line)	$c$ and $l$ intersect at $P$. The procedure returns the second intersection point.
other_incenter(M:Point, A:Point, B:Point)	Let $ABC$ be a triangle and $M$ the incenter of $ABC$. Returns the excenter of $ABC$ on the bisector $CM$.
p3_angle(A:Point, B:Point, C:Point)	Tangens of the angle between $BA$ and $BC$.
p3_circle(A:Point, B:Point, C:Point)	The circle through 3 given points.
p9_center(A:Point, B:Point, C:Point)	Center of the nine-point circle of the triangle $ABC$.
p9_circle(A:Point, B:Point, C:Point)	The nine-point circle (Feuerbach circle) of the triangle $ABC$.
p_bisector(B:Point, C:Point)	The perpendicular bisector of $BC$.
pappus_line(A:Point, B:Point, C:Point, D:Point, E:Point, F:Point)	The Pappus line of a conic 6-tuple of points.
par_line(P:Point, a:Line)	The line through $P$ parallel to line $a$.
par_point(A:Point, B:Point, C:Point)	Point D that makes $ABCD$ a parallelogram.
pc_circle(M:Point, A:Point)	The circle with given center $M$ and circumfere point $A$.
pedalpoint(P:Point, a:Line)	The pedal point of the perpendicular from $P$ onto $a$.
pp_line(A:Point, B:Point)	The line through $A$ and $B$.
radical_axis(c1:Circle, c2:Circle)	The radical axis of two circles, i.e. the line of point with equal pc_degree wrt. to both circles. If the circles intersect this is the line through their intersection points. If the circles don't intersect this are the point with equal tangent segments to both circles.
rotate(C:Point, A:Point, angle:Scalar)	Rotate point A (counterclockwise) around center C with angle angle*Pi.
sqrdist(A:Point, B:Point)	Squared distance between $A$ and $B$.
sqrdist_pl(A:Point, l:Line)	Squared distance between point $A$ and line $l$.
sym_line(a:Line, l:Line)	The line symmetric to $a$ wrt. the line $l$.
sym_point(P:Point, l:Line)	The point symmetric to $P$ wrt. line $l$.
triangle_area(A:Point, B:Point, C:Point)	Signed area of the directed triangle $ABC$.
varpoint(A:Point, B:Point, u:Scalar)	The point $D=(1-u)*A+u*B$ that slides on the line AB, with parameter u.

TSC999

这个工具包其实也没啥好东西，应该是国外某个数学爱好者的作品。译文如下：

TSC999

复平面上解析几何部分公式：

hbghlyj

根据Github链接，作者是莱比锡大学的Hans-Gert Gräbe

hbghlyj

hbghlyj 发表于 2022-4-25 05:13
回复 2# TSC999

除了Mathematica还有在Maple, MuPAD, Reduce平台的工具包
不知内容是否一样