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calculus.py

+import sympy as sp
+import numpy as np
+from functools import reduce
+from sympy import cos, sin, tan, exp, log, pi, E, oo, I, symbols
+from matplotlib import pyplot as plt
+
+"""
+use dict to make more than one equation;
+dict([input().spit("=")])
+"""
+
+# list_color = ['red', 'black', 'yellow', 'blue', 'green', 'purple', 'pink']
+# commands = ["solv", "diff", "integrate",
+#            "tylor_series", "show_tylor", "evalf", "draw", "y"]
+
+help = "help:\n\
+        value(f, {x: 1, y: 2, ...})\n\
+        solve([f, g], [x, y])\n\
+        diff(f, x)\n\
+        integrate(f, (x, sta, end))\n\
+        tylor_series(f, x, x0=0, n=4)\n\
+        draw(f, x, dom=(-10,10), dot_num=200)\n\
+        limit(f, x, lim, dir=\"+\")\n\
+        show_tylor(f, x, dom=(-10,10), x0=0, n=50, dot_num=200, pause_t=0.5)\n\
+        set_var\n\
+        set_var: x, y = symbols('x, y'); f = x ^ 2; ...\n\
+        quit"
+
+x = symbols('x')
+
+
+# def set_var(str):
+#     return exec(input(str).replace("^", "**"))
+
+
+def limit(y, x, lim, dir="+"):
+    return sp.limit(y, x, lim, dir)
+
+
+def value(y, num_x):
+    return y.evalf(subs=num_x)
+
+
+def solve(y, x):
+    return sp.solve(y, x)
+
+
+def diff(y, x):
+    return sp.diff(y, x)
+
+
+def integrate(y, x):
+    return sp.integrate(y, x)
+
+
+def tylor_series(y, x, x0=0, n=4):
+    return sp.series(y, x, x0=x0, n=n)
+
+
+def draw(y, x, dom=(-10, 10), dot_num=200):
+    return show_tylor(y, x, dom, n=0, dot_num=dot_num)
+
+
+def show_tylor(y, x, dom=(-10, 10), x0=0, n=20, dot_num=200, pause_t=0.5):
+
+    # root = tk.Tk()
+    # root.geometry('1000x1000')
+    # frame = tk.Frame(root)
+    # frame.pack(fill="both")
+    # graph = tk.Canvas(frame, width=1000, height=1000)
+    # graph.pack(side="left")
+
+    # step = (dom[1] - dom[0]) / dot_num
+    x_pos = np.linspace(dom[0], dom[1], dot_num + 1, endpoint=True)[1:]
+    plt.ion()
+    plt.grid(True)
+
+    lst_lev = np.array([value(y, i) for i in x_pos])
+    max_y = min(int((np.max(lst_lev) + 2) * 1.5), 100)
+    min_y = max(int((np.min(lst_lev) - 2) * 1.5), -100)
+    plt.plot(x_pos, lst_lev, "b-", linewidth=5)
+
+    plt.xlim(dom[0], dom[1])
+    # plt.xticks(np.linspace(dom[0], dom[1], 21, endpoint=True))
+    plt.ylim(min_y, max_y)
+    # plt.yticks(np.linspace(min_y * 3, max_y * 3, 21, endpoint=True))
+
+    lst_lev = np.zeros(dot_num)
+    factor = 1
+    for lev in range(n):
+        if lev:
+            y = diff(y, x)
+            factor = factor * lev
+        y0 = value(y, x0)
+        lst_lev = lst_lev + \
+            np.array([value(y0 * (x - x0) ** lev / factor,  i) for i in x_pos])
+        plt.plot(x_pos, lst_lev)
+        plt.pause(pause_t)
+        # val = [(i, 500 - lst_lev[i] / step) for i in range(1000)]
+        # graph.create_line(val, fill=list_color[lev % len(list_color)])
+    plt.ioff()
+    plt.show()
+
+    return "successfull!"
+
+
+# try:
+#     y = set_y("(eg:y = x ^ 3 - exp(x) + cos(x) * pi)\ny = ")
+#     cmd = input("value(y, 6), solv(y, x), diff(y, x), integrate(y, (x, sta, end)), \n\
+# tylor_series(y, x, x0=0, n=4), draw(y, x, dom=(-10,10), dot_num=200), limit(y, x, lim, dir=\"+\"), \n\
+# show_tylor(y, x, dom=(-10,10), x0=0, n=50, dot_num=200, pause_t=0.5), quit, resety, y\n\
+# command:")
+# except Exception:
+#     cmd = "err"
+
+# while cmd:
+#     if cmd == "quit":
+#         break
+#     try:
+#         if cmd == "resety":
+#             y = set_y("y = ")
+#         else:
+#             print(eval(cmd))
+
+#     except Exception as err:
+#         print(err)
+#     if 'y' in locals().keys():
+#         cmd = input("command:")
+#     else:
+#         cmd = "resety"
+
+while True:
+    cmd = input("(help):").replace("^", "**")
+    try:
+        if cmd == "quit" or not cmd:
+            break
+        elif cmd == "help":
+            print(help)
+        elif cmd == "set_var":
+            print("eg: x = symbols(\"x\")")
+            print("eg: y = x ^ 3 - exp(x) + cos(x) * pi)")
+            while True:
+                cmd = input("q or enter to quit:")
+                if cmd == "q" or not cmd:
+                    break
+                else:
+                    exec(cmd)
+        elif cmd.startswith("set_var:"):
+            exec(cmd[cmd.find(":") + 1:])
+        else:
+            print(eval(cmd))
+    except Exception as err:
+        print(err)