MATLAB的化简命令:不定化简(simple)
不定化简命令simple综合了前面几种化简方法的有点,但是也略显笨拙。因为它不仅自动将前面每一种化简方法都试了一遍,还尝试了4、5种转化方法,最后还一一将这些结果列了出来。列出的结果往往多的超过3、4屏,用户可细细观察挑选。
下面介绍一下simple命令中的几个转化计算:
combine(trip)
以三角函数的运算性质为主对代数式进行化简。
convert(exp)
将代数式尽量转化为由sin(x)、cos(x)表示的式子。
convert(tan)
将代数式尽量转化为由tan(x)表示的式子。其使用格式为:
simple(A)
例题 将以下两式用不定化简法化简
(1)g=sin2x+cos2x
(2)f=(x2+2x+1)/(x+1)+xcosxtgx
程序如下:
>> syms x
g=sin(x)^2+cos(x)^2;
simple(g)
simplify:
radsimp:
cos(x)^2 + sin(x)^2
simplify(100):
1
combine(sincos):
1
combine(sinhcosh):
cos(x)^2 + sin(x)^2
combine(ln):
cos(x)^2 + sin(x)^2
factor:
cos(x)^2 + sin(x)^2
expand:
cos(x)^2 + sin(x)^2
combine:
cos(x)^2 + sin(x)^2
rewrite(exp):
((1/exp(x*i))/2 + exp(x*i)/2)^2 + (((1/exp(x*i))*i)/2 - (exp(x*i)*i)/2)^2
rewrite(sincos):
cos(x)^2 + sin(x)^2
rewrite(sinhcosh):
cosh(-x*i)^2 - sinh(-i*x)^2
rewrite(tan):
(tan(x/2)^2 - 1)^2/(tan(x/2)^2 + 1)^2 + (4*tan(x/2)^2)/(tan(x/2)^2 + 1)^2
mwcos2sin:
1
collect(x):
cos(x)^2 + sin(x)^2
ans =
1
simplify:
x + x*sin(x)+ 1
radsimp:
(x^2 + 2*x + 1)/(x + 1)+ x*cos(x)*tan(x)
simplify(100):
x + x*sin(x)+ 1
combine(sincos):
(x^2 + 2*x + 1)/(x + 1)+ x*cos(x)*tan(x)
combine(sinhcosh):
(x^2 + 2*x + 1)/(x + 1)+ x*cos(x)*tan(x)
combine(ln):
(x^2 + 2*x + 1)/(x + 1)+ x*cos(x)*tan(x)
factor:
x + x*cos(x)*tan(x)+ 1
expand:
(2*x)/(x + 1)+ 1/(x + 1)+ x^2/(x + 1)+ x*cos(x)*tan(x)
combine:
(x^2 + 2*x + 1)/(x + 1)+ x*cos(x)*tan(x)
rewrite(exp):
(x^2 + 2*x + 1)/(x + 1)- (x*(1/(2*exp(x*i))+ exp(x*i)/2)*(exp(x*2*i)*i i))/(exp(x*2*i)+ 1)
rewrite(sincos):
(x^2 + 2*x + 1)/(x + 1)+ x*sin(x)
rewrite(sinhcosh):
(x^2 + 2*x + 1)/(x + 1)- x*sinh(x*i)*i
rewrite(tan):
(x^2 + 2*x + 1)/(x + 1)- (x*tan(x)*(tan(x/2)^2 - 1))/(tan(x/2)^2 + 1)
mwcos2sin:
(x^2 + 2*x + 1)/(x + 1)+ x*sin(x)
collect(x):
(cos(x)*tan(x)+ 1)*x + 1
ans =
x + x*sin(x)+ 1