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# Effectively disable Linguist
doc/* linguist-vendored
src/* linguist-vendored
*.md linguist-vendored
*.txt linguist-vendored
*.red linguist-vendored
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comment: "Thanks for your report! Unfortunately, we don't use GitHub Issues to manage bug reports for this repository. Instead, please contact the author via [DL2MIE](https://dl2mie.darc.de/)."
issueConfigs:
- content:
- "a2ee3e2e1e0c1b7891c5a390877c070d88745becb9d42d5ecb9cfd03b4dae593367d42ff120b9a836ec944ad242d05b9cc70cac08f13d0f1497dada9b3dc0cfc"
- "4373650124fbaa13f0eebd84723ab2e726dd86284bbee61f93cb22426ed2f1e0643b1765f25c68927d0ee3dcb5ccf9b0c4fbe18b9cb95f8a854e66415810841c"
- "8156afa9af9e68a82b12c3a33cf6110c2376f05be913d0826da9e56363464d8824b66099ece229fabf88cac5a50bab3ee1c2f5ce491c5bc2ca43f4507ede52f9"
- "7c5dc57df185d19fe8656621fa6b5ceaedf04cf9b09968973f8af70095a4b8e4f086a8e75709dc6b28e220d35469c7c1a845c537807f6c98ba6464751f2d051a"
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version: 2
mergeable:
- when: pull_request.opened
name: "Greet a contributor"
validate: []
pass:
- do: comment
payload:
body: >
Thanks for your contribution! Unfortunately, we don't use GitHub pull requests to manage code contributions to this repository. Instead, please contact the author via [DL2MIE](https://dl2mie.darc.de/).
- do: close
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Added .gitignore version [a7ffc6f8bf].
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# REDUCE/Symbolic Scripts
## by Dieter Egger
### Script Descriptions
- Solving equations: `algebra.txt`
- Analyzing functions: `analyze.red`
- Decide on the function to be analyzed, for example `"f:=x**3 - 2*x**2;"`
- Properties: `boolean.txt`
- Analysis: `calculus.txt`
- Physical constants: establish definitions: constants.red; delete definitions: `clear_constants.red`
- Sine, cosine, tangent: `example01.red`
- Binomials, trigonometry, computational accuracy: `example02.red`
- Simple function analysis: `example03.red`
- Simple derivatives: `example04.red`
- Binomials, rules: `example05.red`
- Nested parentheses: `heron.txt`
- Hypergeometry and MeijerG: `hypermeijerg.txt`
- Without LaTeX formatting OK.
- Integration, limits: `integLimit.red`
- Integration: `integral.txt`
- Introduction: `introReduce.txt`
- Linear algebra: `linalg.txt`
- Matrix inversion: `mat.red`
- Computation of space-time metrics
- Metric-tensor from the equation of the hypersurface of a hypersphere, 2-dim: `metric2calc.red`, 3-dim: `metric3calc.red`, 4-dim: `metric4calc.red`
- Riemann, Ricci, Einstein tensors and solution of the field equations, 2-dim: `metric2d.red`, 3-dim: `metric3d.red`, 4-dim: `metric4d.red`
- Dynamic variable names: `mkid.txt`
- Partial fractions: `partialFraction.txt`
- Energy of a photon (requires `constants.red` and `clear_constants.red`): `photonenergy.txt`
- Prefix operators: `prefix.txt`
- Programming: `programming.txt`
- Simple rules: `rules.red`
- Definition of a function: `scalprod.red`
- Speed of light: `speedoflight.txt`
### Homepage
- [DL2MIE](https://dl2mie.darc.de/)
### Links
- [Symbolic for Android](https://play.google.com/store/apps/details?id=de.dieteregger.symbolic)
- [German Script Homepage](https://reduce-algebra.sourceforge.io/tutorials/EggerScripts.php)
- [English Script Homepage](https://reduce-algebra.sourceforge.io/tutorials/EggerScripts.en.php)
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Added SECURITY.md version [4bf8ab023a].
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# Security Information
## Reporting a Vulnerability
Please visit the author's homepage, [DL2MIE](https://dl2mie.darc.de/), for contact details.
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Added doc/MetricUniverse.pdf version [bdfb9288e6].
cannot compute difference between binary files
Added doc/Metrik.pdf version [2a57d66e37].
cannot compute difference between binary files
Added src/algebra.txt version [4a09a9e43d].
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%%%%%%%%%%%%%%%%%%%%%
% ALGEBRA (SOLVE)
%%%%%%%%%%%%%%%%%%%%%
% Solve quadratic equation
solve(x^2+8x+15=0, x);
% Solve for expression
solve(a*log(sin(x+3))^2 - b, sin(x+3));
% Solve simultaneous equations
solve({x+3y=7, y-x=1},{x,y});
% Solve a system with parameters
solve({x=a*z+1, y=b*z},{z,x});
% Simplify expression
((((-r1*(1+k1))/(r2*(1+k2)))+((r1)/(r2)))/(((r1)/(r2))));
% Another solve example
% Note the use of $ as the line termination
% character to suppress output from
% intermediate computations
x1 := sqrt(h^2 + p1^2)$
x2 := sqrt((h/2)^2 + (p-p1)^2)$
x3 := x1 + x2$
dx := df(x3, p1)$
solve(dx, p1);
% Suppose you are given the equation
% x^2+x+1=0 and wish to determine the
% value of x^3. The following simple
% substitution achieves this.
rule := solve(x^2+x+1=0,x)$
y := (x^3 where rule);
% Then y=1, because
% x^3=x*(x^2)=-x*(x+1)=-x^2-x=1.
end;
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Added src/analyze.red version [5edece8dce].
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% function analysis
% Function f (x) is defined ?
if (freeof(f,x)) then << write "first define function f(x)"; end; >>
fp:=df (f, x);
fpp:=df (fp, x);
% zeroes
xz:=solve (f, x);
% extremes
xe:=solve (fp, x);
% reversal points
xr:=solve (fpp, x);
% extreme values
x1:=first (xe);
y1:=sub (x1, f);
y2:=sub (x1, fpp);
on rounded;
if numberp(y2) then
if y2<0 then write "local maximum" else
if y2=0 then write "reversal point"
else write "local minimum";
off rounded;
% integration of 2nd derivative
f1:=int (fpp, x);
% integration of 1st derivative
f0:=int (f1, x);
f0:=int (fp, x);
end;
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Added src/boolean.txt version [62850ba20a].
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n:=3;
if (evenp(n)) then write n," is even" else write n, " is odd";
if (fixp(n)) then write n," is Integer" else write n, " is not Integer";
n:=pi;
if (fixp(n)) then write n," is Integer" else write n, " is not Integer";
n:=3.1;
if (fixp(n)) then write n," is Integer" else write n, " is not Integer";
%
a:=(b+c)^2;
if (freeof(a,b)) then write b," not in ",a else write b," is in ",a;
a:=(c+d)^2;
if (freeof(a,b)) then write b," not in ",a else write b," is in ",a;
%
n:=pi;
if (numberp(n)) then write n," is a number" else write n, " is not a number";
n:=3.1;
if (numberp(n)) then write n," is a number" else write n, " is not a number";
%
if (ordp(n,c)) then write n," before ",c else write n, " after ",c;
n:=z;
if (ordp(n,c)) then write n," before ",c else write n, " after ",c;
%
n:=10;
if (primep(n)) then write n," is prime" else write n, " is not prime";
n:=11;
if (primep(n)) then write n," is prime" else write n, " is not prime";
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Added src/calculus.txt version [4984952ae5].
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%%%%%%%%%%%%%%%%%%%%%
% CALCULUS
%%%%%%%%%%%%%%%%%%%%%
% Specify blue for echoed input
%color("Blue");
% Turn on fancy output
%fancy_output;
% Turn input echo on
%on echo;
% Differentiation
% df/dx
df(x^x,x);
% Multivariate Differentiation
% df/((dx)(dy^2)(dz))
df(x*exp(i*y)*log(z), x, 1, y, 2, z, 1);
% Integration
% indefinite integral with respect to x
int(x^2 + x*sin(x), x);
% SI(x)
int(sin(x)/x,x);
% Integral in interval [-oo, oo]
int(exp(-x^2), x,-infinity,infinity);
% Integral with logarithms
int(log(log(x)),x);
% Turn off echo
%off echo;
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Added src/clear_constants.red version [366dfd4dfc].
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% speed of light
clear(c)$
% Planck's constant
clear(h)$
% elementary charge
clear(el)$
% newtonian constant of gravity
clear(g)$
% Avogadro's number
clear(a)$
% Boltzmann's constant
clear(b)$
% mass of electron
clear(me)$
% mass of neutron
clear(mn)$
% mass of proton
clear(mp)$
% dielectric constant
clear(epsilon0)$
% permeability coefficient mue_0 = 4*pi*1e-7
clear(mu0)$
% Einstein's gravitational constant kappa = 8*pi*G / c^4
clear(kappa)$
% radius of universe [m]
clear(ru)$
% age of universe [s]
clear(tu)$
% critical mass density for a closing universe [cmd]
clear(cmd)$
% astronomical unit
clear(au)$
% Parsec
clear(pc)$
% seconds per sidereal day
clear(sidd)$
% days per tropical year
clear(tropy)$
% Planck mass
clear(pm)$
% Planck time
clear(pt)$
off rounded;
end;
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Added src/constants.red version [3bd159fe32].
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on rounded;
% speed of light
c:=299792458.0$
% Planck's constant
h:=6.62606957E-34$
% elementary charge
el:=1.602176565E-19$
% newtonian constant of gravity
g:=6.67384E-11$
% Avogadro's number
a:=6.02214129E23$
% Boltzmann's constant
b:=1.3806488E-23$
% mass of electron
me:=9.10938291e-31$
% mass of neutron
mn:=1.674927351e-27$
% mass of proton
mp:=1.672621777e-27$
% dielectric constant
epsilon0:=8.85418781762039E-12$
% permeability coefficient mue_0 = 4*pi*1e-7
mu0:=1.25663706143592E-06$
% Einstein's gravitational constant kappa = 8*pi*G / c^4
kappa:=2.076504e-43$
% radius of universe [m]
ru:=1.296120e26$
% age of universe [s]
tu:=4.323391e17$
% critical mass density for a closing universe [cmd]
cmd:=9.568779e-27$
% astronomical unit
au:=149597870700$
% Parsec
pc:=3.08567758149136E+16$
% seconds per sidereal day
sidd:=86164.0991483654$
% days per tropical year
tropy:=365.24219879$
% Planck mass
pm:=2.17650925244531E-08$
% Planck time
pt:=5.3910604238861E-44$
end;
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Added src/example01.red version [26599d6c9f].
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a:=sin (x);
b:=cos (x);
c:=a^2+b^2;
d:=a/b;
f:=tan (x)-d;
trigsimp c;
trigsimp f;
end;
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Added src/example02.red version [db6f1a63d4].
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u:=(x+y+z)^3;
on factor; u;
df(x^x,x);
int(ws,x);
sin(pi/4);
sin(x)^2+cos(x)^2;
trigsimp ws;
v:=sqrt(pi);
on rounded; v;
precision(24); v;
off rounded;
end;
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Added src/example03.red version [f5853dc345].
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% function analysis
f:=3*x^3-7*x^2;
fp:=df (f, x);
fpp:=df (fp, x);
% zeroes
solve (f, x);
% extremes
solve (fp, x);
% reversal points
solve (fpp, x);
% integration of 2nd derivative
f1:=int (fpp, x);
% integration of 1st derivative
f0:=int (f1, x);
f0:=int (fp, x);
end;
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Added src/example04.red version [0addcc0385].
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a:=sin(x);
b:=cos(x);
c:=a+b;
d:=c^2;
% derivative
df(d, x);
% manual derivative
2*(a+b)*(df(a,x)+df(b,x));
end;
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Added src/example05.red version [f430f73384].
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(a+b)^2;
(a+b)^3;
(a+b)^4;
(a+b)^5;
(a+b)^6;
c:=(a+b)^6;
d:=(a+b)^3;
c/d;
a:=sin (x);
b:=cos (x);
c:=a^2+b^2;
d:=a/b;
f:=tan (x)-d;
% Trigo Rules;
trig1:={sin(~x)^2=>(1-cos(x)^2)};
let trig1;
trig2:={tan (~x)=>(sin (x)/cos (x))};
let trig2;
% now with rules;
c;
d;
f;
end;
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a*(b+c*(d+e*(f+g*(h+j*(k+l*(m+n*(o+p*(q+r))))))));
z:=ws;
off factor;
z;
on factor;
z;
end;
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Added src/hypermeijerg.txt version [1bd35ffc38].
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%%%%%%%%%%%%%%%%%%%%%
% HYPERGEOMETRY
% &
% MEIJERG
%%%%%%%%%%%%%%%%%%%%%
% Load special functions 2
load_package specfn2$
% Load generalized hypergeometric package
load_package ghyper$
% Hypergeometric function
hypergeometric({1/2,1},{2},z);
% Load meijerg package
load_package meijerg$
% MeijerG function
% Latex does not work
MeijerG({{}},{{5/4},1},x^2/2);
% without Latex OK
off nat;
MeijerG({{}},{{5/4},1},x^2/2);
on nat;
end;
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Added src/integLimit.red version [849ec37768].
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f:=e^(-x)*sin (x);
int (f, x);
int (f, x, 0, infinity);
int (f, x, 0, b);
sin (b)+cos (b);
c:=sin (b)+cos (b);
limit (c, b,infinity);
limit ((2*x+5)/(3*x-2), x, infinity);
int (e^(-x)*sin (x), x, 0, infinity);
end;
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Added src/integral.txt version [9ab6dc4c0e].
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y:=e^(-x)*sin (x);
int (y, x, 0, infinity);
int (e^(-x)*sin (x), x, 0, infinity);
y;
df (y, x);
int (y, x);
g:=ws;
gup:=limit (g, x, infinity);
glw:=sub (x=0, g);
f:=gup-glw;
end;
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Added src/introReduce.txt version [938a1ca51e].
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% Introduction to Reduce
%
(x+y+z)^2;
for i:= 1:40 product i;
factorial 40;
u := (x+y+z)^2;
df(ws,x);
int(ws,y);
matrix m(2,2);
m := mat((a,b),(c,d));
%
(sin(a+b)+cos(a+b))*(sin(a-b)-cos(a-b))
where cos(~x)*cos(~y) => (cos(x+y)+cos(x-y))/2,
cos(~x)*sin(~y) => (sin(x+y)-sin(x-y))/2,
sin(~x)*sin(~y) => (cos(x-y)-cos(x+y))/2;
%
on fort;
df(log(x)*(sin(x)+cos(x))/sqrt(x),x,2);
off fort;
%
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Added src/linalg.txt version [e9c1c226ce].
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%%%%%%%%%%%%%%%%%%%%%
% LINEAR ALGEBRA
%%%%%%%%%%%%%%%%%%%%%
% Enable fancy output for easier viewing of
% matrix output
%fancy_output$
% Load linear algebra package
load_package linalg$
% Define a complex 3x3 matrix
m1 := mat((1+i*3, 2-i*5, 7-i), (4-i*2, 6+i*9,-8+i*4), (-3-i*7, 3+i*2, -1+i*6));
% Determinant of matrix
write "|m1| = ", det(m1)$
% Trace of matrix
write "trace(m1) = ", trace(m1)$
% Characteristic polynomial
write "characteristic polynomial of m1:";
char_poly(m1,eta);
% Enable real arithmetic
on rounded$
% Singular value decomposition of a matrix.
a := mat((1,3),(-4,3));
write "Singular Value Decomposition of a:"$
svd(a);
off rounded;
end;
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Added src/mat.red version [24a6c2b757].
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% example for matrix inversion
mm:=mat ((1, 19, 9, 5),
(5, 17, 7, 11),
(9, 13, 11, 17),
(13, 7, 15, 19));
mminv:=1/mm;
end;
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% calculation of metric tensor (2-dim space-time)
off echo;
on revpri;
n:=2;
operator x$
x(0):=t; x(1):=lambda0;
% metric
array g(n,n)$
% rules
trig1:={sin(~x)^2=>(1-cos(x)^2)}$ let trig1$
% procedures
procedure scalprod(a,b);
begin integer n;
n:=first(length(a))-1;
result:=for i:=0:n-1 sum a(i)*b(i);
return result
end;
procedure showmatrix(mm);
begin integer m,n;l:=length(mm);m:=first(l)-1;n:=second(l)-1;
matrix hhm(m,n);
for i:=0:m-1 do for j:=0:n-1 do hhm(i+1,j+1):=mm(i,j);
write hhm end;
procedure showvector(vv);
begin integer n;n:=first(length(vv))-1;
matrix hhv(n,1);
for i:=0:n-1 do hhv(i+1,1):=vv(i);
write hhv end;
array f(n+1), dfdt(n+1), dfdl(n+1)$
% current radius
a:=a0*sqrt(1-t^2);
% surface of hyper sphere in t and lambda
f(0):=a*cos(lambda0);
f(1):=a*sin(lambda0);
f(2):=a0*t;
for i:=0:n do dfdt(i):=df(f(i),x(0));
for i:=0:n do dfdl(i):=df(f(i),x(1));
g(0,0):=scalprod(dfdt,dfdt)$
g(0,1):=scalprod(dfdt,dfdl)$
g(1,0):=scalprod(dfdl,dfdt)$
g(1,1):=scalprod(dfdl,dfdl)$
write "f = "; showvector(f);
write "df/dt = "; showvector(dfdt);
write "df/dl = "; showvector(dfdl);
write "g = "; showmatrix(g);
off revpri;
on echo;
end;
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Added src/metric2d.red version [041b81ff2e].