219 lines
7.5 KiB
Python
219 lines
7.5 KiB
Python
from flask import Flask, render_template, request, redirect, Response
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from sympy import *
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from helpers import apology
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import numpy as np
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app = Flask(__name__)
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# Convert our commonly used variables into sympy symbols
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x, y, z, t, X, Y, Z, T = symbols('x y z t X Y Z T')
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@app.route('/')
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def hello():
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return render_template('index.html')
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@app.route('/differentiation', methods=['GET', 'POST'])
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def differentiation():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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f = request.form.get("function")
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Differentiate and return latex expressions
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fprime = latex(f.diff(x))
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value = latex(f)
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return render_template("differentiated.html", value=value, fprime=fprime)
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else:
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return render_template("differentiation.html")
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@app.route("/integration", methods=["GET", "POST"])
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def integration():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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f = request.form.get("function")
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Integrate and return latex expressions
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fintegral = latex(f.integrate(x))
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value = latex(f)
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return render_template("integrated.html", value=value, fintegral=fintegral)
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else:
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return render_template("integration.html")
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@app.route("/riemann", methods = ["GET", "POST"])
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def riemann():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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if not request.form.get("lowerbound"):
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return apology("must provide a lower bound", 400)
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if not request.form.get("upperbound"):
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return apology("must provide an upper bound", 400)
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if not request.form.get("subintervals"):
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return apology("must provide a number of subintervals", 400)
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if not request.form.get("sumtype"):
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return apology("must choose left or right", 400)
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# Get our info from form
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f = request.form.get("function")
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sumtype = request.form.get("sumtype")
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lb = int(request.form.get("lowerbound"))
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ub = int(request.form.get("upperbound"))
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si = int(request.form.get("subintervals"))
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Run through Riemann Sum algorithm, creatings lists for display
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# of inputs, outputs, and areas (their products)
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value = latex(f)
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dx = round((ub - lb) / si, 3)
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inputs = list()
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if sumtype == "1":
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for i in range(0, si):
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inputs.append(round(dx * (i), 3))
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if sumtype == "2":
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for i in range(0, si):
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inputs.append(round(dx * (i + 1), 3))
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outputs = list()
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for input in inputs:
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temp = f.subs(x, input)
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outputs.append(round(temp, 3))
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rectangles = list()
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for output in outputs:
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temp = output * dx
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rectangles.append(round(temp, 3))
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result = round(sum(rectangles), 3)
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# Choose template based on left or right sum
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if sumtype == "1":
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return render_template("summed.html", value=value, sumtype=sumtype, lb=lb, ub=ub, si=si, dx=dx,
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inputs=inputs, outputs=outputs, rectangles=rectangles, result=result)
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else:
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return render_template("rightSummed.html", value=value, sumtype=sumtype, lb=lb, ub=ub, si=si, dx=dx,
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inputs=inputs, outputs=outputs, rectangles=rectangles, result=result)
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else:
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return render_template("riemann.html")
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@app.route("/maxmin", methods=["GET", "POST"])
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def maxmin():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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if not request.form.get("lowerbound"):
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return apology("must provide a lower bound", 400)
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if not request.form.get("upperbound"):
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return apology("must provide an upper bound", 400)
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# Get input from form
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f = request.form.get("function")
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lb = round(sympify(request.form.get("lowerbound")), 3)
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ub = round(sympify(request.form.get("upperbound")), 3)
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Get Derivative, solve for real solutions, update candidates list
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fprime = f.diff(x)
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solutions = list()
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solutions.append(round(f.subs(x,0), 3))
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candidates = list()
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for solution in solutions:
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candidates.append(solution)
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candidates.append(lb)
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candidates.append(ub)
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# Fill values list with solutions
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values = list()
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for candidate in candidates:
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temp = round(f.subs(x, candidate), 3)
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values.append(temp)
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# Find max/min of values
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maximum = max(values)
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newvar = min(values)
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# Turn all into latex
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value = latex(f)
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fprime = latex(fprime)
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for i, solution in enumerate(solutions):
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solutions[i] = latex(solution)
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return render_template("optimized.html", value=value, fprime=fprime, solutions=solutions, lb=lb, ub=ub,
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candidates=candidates, newvar=newvar, values=values, maximum=maximum)
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else:
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return render_template("maxmin.html")
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@app.route("/aprox", methods=["GET", "POST"])
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def aprox():
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if request.method == "POST":
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# Check if inputs were given
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if not request.form.get("function"):
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return apology("must provide a function", 400)
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if not request.form.get("easy"):
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return apology("must provide an easy value", 400)
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if not request.form.get("hard"):
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return apology("must provide a difficult value", 400)
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# Get inputs, sympify them, and check to see if valid
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f = request.form.get("function")
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a = request.form.get("easy")
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h = request.form.get("hard")
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# Setup our symbols for SymPy
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f = setup_symbols(f)
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# Make sure a and h are numbers
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a = sympify(a)
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h = sympify(h)
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if not a.is_number:
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return apology("easy value must be a number", 400)
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if not h.is_number:
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return apology("difficult value must be a number", 400)
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a = round(a, 3)
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h = round(h, 3)
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# Run through Linearization algorithm
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fprime = f.diff(x)
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fa = round(f.subs(x, a), 3)
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fprimea = round(fprime.subs(x, a), 3)
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lh = round(fa + fprimea*(float(h)-float(a)), 3)
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# Convert to latex for MathJax reading
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value = latex(f)
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fprime = latex(fprime)
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fa = latex(fa)
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lh = latex(lh)
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return render_template("aproxd.html", value=value, fprime=fprime, a=a, h=h, fa=fa, fprimea=fprimea, lh=lh)
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else:
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return render_template("aprox.html")
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def errorhandler(e):
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"""Handle error"""
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if not isinstance(e, HTTPException):
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e = InternalServerError()
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return apology(e.name, e.code)
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def setup_symbols(f):
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f = sympify(f)
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# replace commonly used variables with x
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for letter in [x, y, z, t, X, Y, Z, T]:
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f = f.subs(letter, x)
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return f
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if __name__ == '__main__':
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app.run()
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