https://maxima-discuss.narkive.com/3g8egf0q/makelist-vs-create-list
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maxima command
algebra
ratsimp() 化簡
expand() 展開
factor() 因式分解kill(x) kill the x variable
kill(all) kill all variables
x:123 assign x=123
f(x):=x^2＋2*x+1 define function of x =x^2+2x+1
sum(i,i,1,10) sum i , i from 1 to 10
%i image number
%pi
%e
%phi the golden mean (1+sqrt(5))/2
%gamma the Euler-Mascheroni constant
inf real positive inifinity
minf real negative inifinity
abs() absolute
sqrt() square root
float() float number
compare() compare numbers
is()
load("filename")
solve([equation],[variable])
round()
floor()
print()
%i1) powerdisp;
(%o1) false
(%i2) x^2+2*x+1;
2
(%o2) x + 2 x + 1
(%i3) powerdisp: true;
(%o3) true
(%i4) x^2+2*x+1;
2
(%o4) 1 + 2 x + x
(%o1) false
(%i2) x^2+2*x+1;
2
(%o2) x + 2 x + 1
(%i3) powerdisp: true;
(%o3) true
(%i4) x^2+2*x+1;
2
(%o4) 1 + 2 x + x
radexpand
evaluate
Default value: true
radexpand controls some simplifications of radicals.
When radexpand is all, causes nth roots of factors of a product
which are powers of n to be pulled outside of the radical. E.g. if
radexpand is all, sqrt (16*x^2) simplifies to 4*x.
More particularly, consider sqrt (x^2).
- If
radexpandisallorassume (x > 0)has been executed,sqrt(x^2)simplifies tox. - If
radexpandistrueanddomainisreal(its default),sqrt(x^2)simplifies toabs(x). - If
radexpandisfalse, orradexpandistrueanddomainiscomplex,sqrt(x^2)is not simplified.
Note that domain only matters when radexpand is true
reference
https://maxima.sourceforge.io/docs/manual/maxima_46.html.
evaluate
8.1 Functions and Variables for Evaluation
4.2 Functions and Variables for Command Line
3. Entering commands
ctl-j
ctl-u
alt-p to search backwards
alt-n to search forward
cabs absolute of complex number
conjugate
carg angle of complex number
realpart
imagpart
polarform
rectform
For further ways to compute with complex numbers, see the functions
rectform, realpart, imagpart,
carg, conjugate and polarform.
Matrix
matrix()
determinant()
invert()
transpose()
length()
Plot
plot2d([equation],[x,lower, upper])
plot3d([equation],[x,lower,upper],[y,lower,upper])
vector
https://maxima.sourceforge.io/docs/manual/maxima_116.html#Vectors
a.b a dot b
axb a cross b
load("vect" );
express(a~b);
https://maxima.sourceforge.io/docs/manual/maxima_131.html#Sums-Products-and-Series
permutation/ combination
load(functs)
permutation (n, r)
combination (n, r)
sequence/ series
arithmetic (a, d, n)
geometric (a, r, n)
harmonic (a, b, c, n)
geosum (a, r, n)
Set
https://maxima.surceforge.io/docs/manualo/maxima_156.html#Sets
Differential/Integrate
diff()
integrate()
limit()
2021年1月10日 星期日
2021年1月5日 星期二
maxima vector command
Maxima vector magnitude and cross product
https://math.stackexchange.com/questions/1029762/maxima-vector-magnitude-and-cross-product/1180712
http://www.scotchildress.com/wxmaxima/VectorArithmetic/VectorArithmetic.html
vector command in maxima
- a.b a.b;
- axb
load("vect" );
express(a~b);
- |a|
sqrt(a.a);
or
norm(x):=sqrt(x.x);
- a hat
a/sqrt(a.a) ;
or
hat(x):=x/norm(x);
- a proj b
proj(a,b):=a.b/norm(b)^2 *b ;
example:
kill(all);
load("vect" );
express(a~b);
norm(x):=sqrt(x.x);
hat(x):=x/norm(x);
proj(a,b):=a.b/norm(b)^2 *b ;
a:[1,2];
b:[3,4];
a.b;
express(a~b);
norm(a);
hat(a);
proj(a,b);
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微分應用
數c
IV 13 回
(3-4
微分應用)
109.4.21
3.2
f(x):=-x^2+6*x-8; has max or min?
g:diff(f(x));
solve(g);
4.
f(x):=3*x-x^3; has max , min=?
g:diff(f(x));
solve(g);
f(1);
f(-1);
calculate
1.
f(x)=3+4*x-x^2, 圖形,
遞增
遞減的區域
f(x):=3+4*x-x^2;
g:diff(f(x));
solve(g);
2.
x+y=30, solve (xy)max=?
x,x-30
x,x-30
f(x):=x(x-30);
g:diff(f(x));
solve(g);
g:diff(f(x));
solve(g);
3.f(x)=2x^3+ax^2+bx+25
,x=-3,x=2 has
related extreme value, solve a,b=?
related extreme value, solve a,b=?
f(x):=2*x^3+a*x^2+b*x+25;
g:diff(f(x),x);
4.
f(x)=5x^2+4x+1,x=a has fmin=b, solve
a,b=?
a,b=?
2020年4月20日 星期一
2018年5月27日 星期日
maxima教學
Edwin L. (Ted) Woollett
屏東教育大學
屏東教育大學 應數系
http://www.math.nptu.edu.tw/ezfiles/115/1115/img/626/JHmathG11.pdf
De Morgan Law (迪摩根定理)
(AUB)'=A'nB'
(AnB)'=A'U B'
U:{1,2,3,4,5,6,7,8,9,10};
A:{1,2,4,6};B:{1,3,4};
Ap:setdifference(U,A);
Bp:setdifference(U,B);
AuB;union(A,B);
AnB:intersect(A,B);
setdifference(U,AuB);
intersect(Ap,Bp);
setdifference(U,AnB);
union(Ap,Bp);
屏東教育大學
屏東教育大學 應數系
http://www.math.nptu.edu.tw/ezfiles/115/1115/img/626/JHmathG11.pdf
施文奇的教學檔案
De Morgan Law (迪摩根定理)
(AUB)'=A'nB'
(AnB)'=A'U B'
U:{1,2,3,4,5,6,7,8,9,10};
A:{1,2,4,6};B:{1,3,4};
Ap:setdifference(U,A);
Bp:setdifference(U,B);
AuB;union(A,B);
AnB:intersect(A,B);
setdifference(U,AuB);
intersect(Ap,Bp);
setdifference(U,AnB);
union(Ap,Bp);
2018年4月11日 星期三
maxima website
Mathematical Science & TechnologiesMaxima for Symbolic Computationhttp://mathscitech.org/articles/maxima#book |
2018年4月10日 星期二
集合,等比數列,等差數列,permutation,combination
集合(Set)
U:{1,2,3,4,5,6,7,8,9,10};
A:{1,2,4,6};B:{1,3,4};
AnB:intersect(A,B);
powerset(A);
Bp:setdifference(U,B);
AminusB:setdifference(A,B);
BminusA:setdifference(B,A);
ApnBp:intersect(Ap,Bp);
ApuBp:union(Ap,Bp);
setequalp (a, b)
Returns
setequalp(setdifference(U,AuB),ApnBp);
setequalp(setdifference(U,AnB),ApuBp);
排列(permutation), 組合(combination)
permutation(5,3);
combination(5,3);
級數和
U:{1,2,3,4,5,6,7,8,9,10};
A:{1,2,4,6};B:{1,3,4};
cardinality(U);
cardinality(A);
cardinality(B);
AuB:union(A,B);
AnB:intersect(A,B);
powerset(A);
cardinality(%);
Ap:setdifference(U,A); Bp:setdifference(U,B);
AminusB:setdifference(A,B);
BminusA:setdifference(B,A);
ApnBp:intersect(Ap,Bp);
ApuBp:union(Ap,Bp);
true if sets a and b have the same number of elements
and is(x = y) is true
for x in the elements of a
and y in the elements of b,
considered in the order determined by listify.
Otherwise, setequalp returns false.
setequalp(setdifference(U,AuB),ApnBp);
setequalp(setdifference(U,AnB),ApuBp);
disjoin(A,B);
disjoin(B,A);
http://maxima.sourceforge.net/docs/manual/maxima_35.html#SEC188
排列(permutation), 組合(combination)
- Function: permutation (n, r)
- Returns the number of permutations of r objects
selected from a set of n objects.
To use this function write firstload(functs).
- Function: combination (n, r)
- Returns the number of combinations of n objects
taken r at a time.
To use this function write firstload(functs).
Categories: Package functs · Mathematical functions
load(functs);permutation(5,3);
combination(5,3);
級數和
- Function: arithmetic (a, d, n)
- Returns the n-th term of the arithmetic series
a, a + d, a + 2*d, ..., a + (n - 1)*d.
To use this function write firstload(functs).
Categories: Package functs · Sums and products
- Function: geometric (a, r, n)
- Returns the n-th term of the geometric series
a, a*r, a*r^2, ..., a*r^(n - 1).
To use this function write firstload(functs).
Categories: Package functs · Sums and products
- Function: harmonic (a, b, c, n)
- Returns the n-th term of the harmonic series
a/b, a/(b + c), a/(b + 2*c), ..., a/(b + (n - 1)*c).
To use this function write firstload(functs).
Categories: Package functs · Sums and products
- Function: arithsum (a, d, n)
- Returns the sum of the arithmetic series from 1 to n.
To use this function write firstload(functs).
Categories: Package functs · Sums and products
- Function: geosum (a, r, n)
- Returns the sum of the geometric series from 1 to n. If n is
infinity (
inf) then a sum is finite only if the absolute value of r is less than 1.
To use this function write firstload(functs).
load(functs);
a:1;d:2;n:10;
arithmetic(a,d,n);
/*an=a+(n-1)d*/
a+(n-1)*d;
r:2;n:10;
geometric (a, r, n) ;
/*an=ar^(n-1)*/
a*r^(n-1);
b:2;c:3;
harmonic (a, b, c, n);
d:2;n:10;
arithsum (a, d, n);
/*a+(a+d)+(a+2d)+...+(a+(n-1)d) */
/*Sn=n/2(2a+(n-1)d) */
n/2*(2*a+(n-1)*d);
r:2;n:10;
geosum (a, r, n);
/*a+ar+ar^2+...+ar^(n-1) */
/* Sn=a(1-r^n)/(1-r) */
a*(1-r^n)/(1-r);
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