@@ -1154,9 +1154,14 @@ plt.title('3D plot of $z = x^2 + y^2$')
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11551155* 使用np.linspace()使t ∈ [ 0,2π] 。 然后给 (Use np.linspace0 to make t ∈ [ 0,2π] . Then give)
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1157- ![ 2] ( https://github.com/MurphyWan/Python-first-Practice/blob/master/images/3days_img017_2.jpg )
1157+ 1158+ ![ 2] ( https://github.com/MurphyWan/Python-first-Practice/blob/master/images/3days_img017_2.jpg )
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1159- - 针对X绘Y。 在这个情节中添加一个称为"Heart"的标题。 (Plot y against x. Add a title to this plot which is called "Heart" .)
1160+ 1161+ 1162+ - 针对X绘Y。 在这个情节中添加一个称为"Heart"的标题。 (Plot y against x. Add a title to this plot which is called "Heart" .)
1163+ 1164+ 11601165
11611166* 针对x∈[ -10,10] , y∈[ -10,10] , 绘制3D函数 (Plot the 3D function for x∈[ -10,10] , y∈[ -10,10] )
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@@ -1170,7 +1175,7 @@ plt.title('3D plot of $z = x^2 + y^2$')
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1173- 1178+ ## Sympy
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@@ -1184,12 +1189,20 @@ plt.title('3D plot of $z = x^2 + y^2$')
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1192+ 1193+ 11871194``` python
11881195```
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1199+ ## 符号计算 (Symbolic computation)
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1201+ * 到目前为止,我们只考虑了数值计算。 (So far, we only considered the numerical computation.)
1202+ 1203+ * Python也可以通过模块表征进行符号计算。(Python can also work with symbolic computation via module sympy.)
1204+ 1205+ * 符号计算可用于计算方程,积分等的显式解。 (Symbolic computation can be useful for calculating explicit solutions to equations, integrations and so on.)
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@@ -1199,8 +1212,24 @@ plt.title('3D plot of $z = x^2 + y^2$')
11991212```
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12011214
1215+ ## 声明一个符号变量 (Declare a symbol variable)
1216+ 1217+ ``` python
1218+ 1219+ import sympy as sy
12021220
1221+ # 声明x,y为变量
1222+ x = sy.Symbol(' x'
1223+ y = sy.Symbol(' y'
1224+ a, b = sy.symbols(' a b'
12031225
1226+ # 创建一个新符号(不是函数
1227+ f = x** 2 + 2 - 2 * x + x** 2 - 1
1228+ print (f)
1229+ # 自动简化
1230+ g = x** 2 + 2 - 2 * x + x** 2 - 1
1231+ print (g)
1232+ ```
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@@ -1210,8 +1239,23 @@ plt.title('3D plot of $z = x^2 + y^2$')
12101239```
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1242+ ## Use of symbol 1: Solve equations
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1244+ ``` python
12141245
1246+ import sympy as sy
1247+ 1248+ x = sy.Symbol (' x'
1249+ y = sy.Symbol(' y'
1250+ # give [-1, 1]
1251+ print (sy.solve (x** 2 - 1 ))
1252+ # no guarantee for solution
1253+ print (sy.solve(x** 3 + 0.5 * x** 2 - 1 ))
1254+ # exepress x in terms of y
1255+ print (sy.solve(x** 3 + y** 2 ))
1256+ # error: no algorithm can be found
1257+ print (sy.solve(x** x + 2 * x - 1 ))
1258+ ```
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@@ -1221,8 +1265,46 @@ plt.title('3D plot of $z = x^2 + y^2$')
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1268+ ## Use of symbol 2: Integration
1269+ 1270+ ``` python
1271+ import sympy as sy
1272+ x = sy.Symbol(' x'
1273+ y = sy.Symbol( ' y'
1274+ b = sy.symbols ( ' a b'
1275+ # single variable
1276+ f = sy.sin(x) + sy.exp(x)
1277+ print (sy.integrate(f, (x, a, b)))
1278+ print (sy.integrate(f, (x, 1 , 2 )))
1279+ print (sy.integrate(f, (x, 1.0 ,2.0 )))
1280+ # multi variables
1281+ g = sy.exp(x) + x * sy.sin(y)
1282+ print (sy.integrate(g, (y,a,b)))
1283+ ```
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12271287``` python
12281288```
1289+ 1290+ 1291+ ## Use of symbol 2: Differentiation
1292+ 1293+ ``` python
1294+ import sympy as sy
1295+ x = sy.Symbol( ' x'
1296+ y = sy.Symbol( ' y'
1297+ # sing1e variable
1298+ f = sy.cos(x) + x** x
1299+ print (sy . diff (f , x))
1300+ # multi variables
1301+ g = sy.cos(y) * x + sy.log(y)
1302+ print (sy.diff (g, y))
1303+ ```
1304+ 1305+ 1306+ ``` python
1307+ 1308+ 第二天结束,辛苦了
1309+ 1310+ ```
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