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SolveTools[CancelInverses] - 互いに逆となる関数を約することでの式の正規化
使い方
CancelInverses(expr)
パラメータ
expr - 式
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説明
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CancelInverses(expr) 関数は、互いに逆となる関数の打ち消しを実行します。
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trig(arctrig(subexpr)) -> subexpr
arctrig(trig(subexpr)) -> subexpr
ln(exp(subexpr)) -> subexpr
exp(ln(subexpr)) -> subexpr
ln(LambertW(exp(subexpr))) -> subexpr - LambertW(exp(subexpr))
exp(integer*LambertW(subexpr)) -> subexpr^integer/LambertW(subexpr)^integer
1-sin(subexpr)^2 -> cos(subexpr)^2
1-cos(subexpr)^2 -> sin(subexpr)^2
subexpr^(1/2) -> sqrt(subexpr)
(subexpr^rational)^integer -> subexpr^(rational*integer)
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前述の簡単化の組合せも作成されます。また、2つの引数の arctan は、sin(subexpr) を含む場合に簡単化されます。
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注意: 全ての簡単化が、どこでも有効となるわけではありません。CancelInverses を呼び出す際には、注意が必要です。
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例
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with(SolveTools):
CancelInverses(1+exp(-x^2));
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| (2.1) |
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CancelInverses(arccos(cos(x-y*2)));
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| (2.2) |
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CancelInverses(tan(arctan(x-y*2)));
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| (2.3) |
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CancelInverses(ln(exp(x-y*2)));
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| (2.4) |
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CancelInverses(exp(ln(x-y*2)));
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| (2.5) |
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CancelInverses(ln(LambertW(exp(a+b^2+c^3))));
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| (2.6) |
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CancelInverses(exp(LambertW(a+b^2+c^3)));
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| (2.7) |
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CancelInverses(g(1-cos(x+y+z)^2));
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| (2.8) |
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CancelInverses((-5)^(1/2));
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| (2.9) |
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CancelInverses(((x*sin(x))^(1/2))^3);
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| (2.10) |
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CancelInverses(exp(ln(x)+ln(y+z)+t));
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| (2.11) |
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CancelInverses(exp(2*ln(x)+3*ln(y+z)-4*t));
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| (2.12) |
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CancelInverses(exp(2*ln(sin(x))));
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| (2.13) |
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CancelInverses(ln(exp(c*k)^z*exp(b*t)));
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| (2.14) |
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CancelInverses(ln(z^(3/2)*x));
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| (2.15) |
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CancelInverses(ln((z^(3/2))^5*x));
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| (2.16) |
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CancelInverses(ln(exp(z)^cos(x)));
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| (2.17) |
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CancelInverses(ln((s^f(x))^g(z)));
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| (2.18) |
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CancelInverses(x^((x+1)/ln(x)+(x-1)/ln(x)));
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| (2.19) |
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CancelInverses(arctan(-sin(b), cos(b)));
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| (2.20) |
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CancelInverses(arctan(cos(b), sin(b)));
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| (2.21) |
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