init

Author: q1zhen

main.py

@@ -0,0 +1,100 @@
+from sympy import *
+from sympy.parsing.sympy_parser import T
+from flask import Flask, render_template, request, jsonify
+
+C = {
+	"pi": {
+		"ex": lambda x, n, p: ( x**n * (1-x)**n * (p[0] + p[1]*x + p[2]*x**2) ) / ( 1 + x**2 ),
+		"inner": lambda x, n, p: p[0] + p[1]*x + p[2]*x**2,
+	},
+	"e": {
+		"ex": lambda x, n, p: x**n * (1 - x)**n * (p[0] + p[1]*x) * E**x,
+		"inner": lambda x, n, p: p[0] + p[1]*x,
+	}
+}
+
+def above0(inner, n, params, prec=1000):
+	for i in range(0, prec):
+		x = i / prec
+		if inner(x, n, params) <= 0:
+			return False
+	return True
+
+def getEq(ex, n, params, collects):
+	x = symbols("x")
+	r = collect(simplify(integrate(ex(x, n, params), (x, 0, 1))).expand(), collects, evaluate=False)
+	return {
+		str(key): dict(sorted({
+			str(k): str(v) for k, v in collect(value, params, evaluate=False).items()
+		}.items())) for key, value in r.items()
+	}
+
+# print(getEq(C["pi"]["ex"], [1, a, b, c], [a, b, c], ["log(2)", "pi"]))
+
+def generate(ex, inner, params, desired):
+	collects = [i for i in desired if i != "1"]
+	for i in range(100):
+		eqs = getEq(ex, i, params, collects)
+		matrix = [
+			[
+				eqs[k].get(str(e)) if eqs[k].get(str(e)) != None else 0
+				for e in params
+			] + [v]
+			for k, v in desired.items()
+		]
+		solution = solve_linear_system(Matrix(matrix), *params)
+		if above0(inner, i, list(solution.values())):
+			return i, solution
+
+def main(mode, value):
+	global C
+	if mode == "pi":
+		a, b, c, x = symbols("a b c x")
+		v = parse_expr(value, transformations=T[:])
+		piGreater = N(pi) > N(v)
+		n, sol = generate(C["pi"]["ex"], C["pi"]["inner"], [a, b, c], {
+			"log(2)": 0,
+			"pi": 1 if piGreater else -1,
+			"1": -v if piGreater else v
+		})
+		r = simplify(C["pi"]["ex"](x, n, list(sol.values())))
+		return " ".join([
+			"\\int_0^1", latex(r), "\\textrm{d} x =",
+			f"\\pi - {latex(parse_expr(value))}" if piGreater else f"{latex(parse_expr(value))} - \\pi",
+			"> 0"
+		])
+	elif mode == "e":
+		a, b, x = symbols("a b x")
+		v = parse_expr(value, transformations=T[:])
+		eGreater = N(E) > N(v)
+		n, sol = generate(C["e"]["ex"], C["e"]["inner"], [a, b], {
+			"E": 1 if eGreater else -1,
+			"1": -v if eGreater else v
+		})
+		r = simplify(C["e"]["ex"](x, n, list(sol.values())))
+		return " ".join([
+			"\\int_0^1", latex(r), "\\textrm{d} x =",
+			f"e - {latex(parse_expr(value))}" if eGreater else f"{latex(parse_expr(value))} - e",
+			"> 0"
+		])
+
+
+app = Flask(__name__)
+
+@app.route('/', methods=['GET'])
+def index():
+    return render_template('index.html')
+
+@app.route('/process', methods=['POST'])
+def process():
+	user_input = request.form['input_box']
+	mode = request.form['mode']
+	try:
+		result = main(mode, str(user_input))
+	except Exception as e:
+		result = "ERROR"
+	return jsonify(result=result)
+
+if __name__ == '__main__':
+    app.run(debug=True)
+

params.py

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+from sympy import *
+import tqdm
+import json
+
+x = symbols("x")
+a, b, c = symbols("a b c")
+
+ex = lambda n: ( x**n * (1-x)**n * (a + b*x + c*x**2) ) / ( 1 + x**2 )
+params = {}
+
+for n in tqdm.tqdm(range(1, 21)):
+	r = collect(simplify(integrate(ex(n), (x, 0, 1))).expand(), [pi, log(2)], evaluate=False)
+	params[str(n)] = {str(key): {
+		str(k): str(v) for k, v in collect(value, [a, b, c], evaluate=False).items()
+	} for key, value in r.items()}
+
+with open("params_pi.json", "w+") as f:
+	json.dump(params, f, indent="\t")
+
+