maple-xの一次の項と定数項の係数を選ぶ方法
xの係数がこれこれ、定数項の係数がこれこれとするやりかた
r := (-3161*a+59*b+147036)*x+2160*a-40*b-100489;
solve({coeff(r,x)=2,coeff(r,x,0)=1},{a,b});
説明: coeff(r,x)=2は式rの中のxの係数が2, coeff(r,x,0)=1は式rのx^0(つまり定数)の
係数が1、そうなるようなa,bを求めるということ
数学-極座標系の二点間の距離
極座標系の二点の距離
2次元の極座標の例ですが
点P = (r,θ)
点Q = (q,φ) の距離の二乗は
r^2+q^2-2qr*cos(θ-φ) で得られます
実際
点P,Qの極座標表示をxy座標に直すと
P = ( rcos(θ), rsin(θ))
Q = ( qcos(φ), qsin(φ))
よって二点間の距離の二乗は
(rcos(θ)-qcos(φ))^2+(rsin(θ)-qsin(φ))^2
= r^2+q^2-2qr{cos(θ)cos(φ)+sin(θ)sin(φ)}
= r^2+q^2-2qr*cos(θ-φ)
になります
http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1343924698
数学-r = 1 + cos(theta/2)
r = 1 + cos(theta/2)のグラフ
https://www.youtube.com/watch?v=E7oR_JBgUzA
maple-mapleのplot
a:= x^2 - abs(x):
plot(a,x=-2 .. 2);
b := x * sin(x): plot(b,x = -Pi .. Pi);
c := 2 * sin(x) + sin(2*x): plot(c , x = 0 .. 2*Pi);
d:= exp( - x^2): plot(d, x = -infinity .. infinity);
f:= x -> if abs(x) <= 1 then abs(abs(x) - 1) else 0 fi;
x -> if |x| <= 1 then ||x| - 1| else 0 fi;
plot(f(x), x = -3 .. 3);
Error, (in f) cannot determine if this expression is true or false: abs(x) <= 1
f(3);
0
f(0);
1
g := proc(x)
if abs(x) <= 1 then abs(abs(x) - 1)
else 0
fi
end proc;
proc(x) ... end;
plot('g(x)', x = -3..3);
h := proc(x)
if abs(x) > 1 then x^2
elif abs(x) = 1 then 0
else - x^2
fi
end proc;
proc(x) ... end;
plot(h, -2..2, -10 .. 10);
h(1);
x -> 0
plot({seq( x^j , j = 1 .. 4)}, x = -1.5 .. 1.5);
plot({seq( sin(k*x) , k = 1 ..4)}, x = 0 .. Pi, title = 'sin
( kx ) \in [-Pi, Pi]');
plot([cos(t), sin(t), t = 0 .. Pi], scaling = constrained);
plot([3*t/(1 + t^3), 3*t^2/(1 + t^3), t = -5 .. 5], -2 .. 2, -5 .. 5);
?polarplot
with(plots):
polarplot(3*cos(x), x = 0 .. 2*Pi);
polarplot([1+cos(t),t,t= -Pi .. Pi]);
plot([1+cos(t),t,t= -Pi .. Pi], coords=polar, scaling = constrained);
plot([t,Pi/3, t = -infinity .. infinity], 0 .. 5, 0 .. 5, coords = polar, scaling = constrained);
plot([cos(t), t, t = -Pi/2 .. Pi/2], coords = polar, scaling = constrained);
plot([1 + cos(t), t, t = -Pi .. Pi], coords = polar, scaling = constrained);
polarplot([(sin(t/3))^3, t, t= 0 .. Pi], scaling = constrained);
plot([1+t, t, t = 0 .. Pi/2], coords = polar, scaling = constrained);
polarplot([1+t, t, t = 0 .. Pi/2], scaling = constrained);
polarplot([sqrt(cos(2*t)), t, t = -Pi .. Pi]);
with(plots):implicitplot(x^2 + y^2=1 , x = -2 .. 2, y = -2 .. 2, scaling = constrained);
implicitplot(y^2 = x, x = -10..10, y = - 5 .. 5, scaling = constrained);
implicitplot(y^2 = x*(x-1), x = -3 .. 3, y = -9 .. 9, numpoints = 500000);
with(plots):implicitplot(x^3 - 3*x*y + y^3 = 0, x = -5 .. 5, y = -5 .. 5, numpoints = 20000);
implicitplot(9*x^2 + 24*x*y + 16*y^2 - 26*x + 7*y - 34 = 0, x = -10 .. 10, y = -10 .. 10, numpoints = 10000);
plot3d(sin(x^2 + y^2), x = -Pi/2 .. Pi/2, y = -Pi/2 .. Pi/2);
plot3d(x^2 + y^2, x = -2 ..2, y = -2 ..2);
maple-expression sequenceを作る_素数を選ぶ
expression sequenceをつくる, sequenceから選ぶ
$1..5
で1, 2, 3, 4, 5ができる
# sequenceから選ぶ
select(isprime, [$100..150]);%sequenceから選ぶ
# i番目の素数のsequenceを作る
seq(ithprime(k), k = 1 ..20);
maple-sumとproduct
sumとproductについて
seq(Sum(k^j, k = 1 .. n)= factor(sum(k^j, k = 1 .. n)),j = 1 .. 10);
Sum(k, k = 1 .. n):
% = factor(value(%));
#valueはSumというinertフォームを活性化するために使う。
Product(i,i=1..10):%=value(%);
Product(x - a[j],j=1..5): %=value(%);
差積は
n:=10:product(product(x[i] - x[j],j=i+1..n),i=1..n - 1);