Expression of type Lambda ¶

from the theory of proveit.trigonometry ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, a, b, r
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Exp, Mult, Real, e, frac, i, subtract, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Abs(subtract(Mult(r, Exp(e, Mult(i, a))), Mult(r, Exp(e, Mult(i, b))))), Mult(two, r, Sin(frac(Abs(subtract(a, b)), two)))), And(InSet(a, Real), InSet(b, Real))))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a, b\right) \mapsto \left\{\left|\left(r \cdot \mathsf{e}^{\mathsf{i} \cdot a}\right) - \left(r \cdot \mathsf{e}^{\mathsf{i} \cdot b}\right)\right| = \left(2 \cdot r \cdot \sin{\frac{\left|a - b\right|}{2}}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	50, 57
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 37 operand: 18
10	Operation	operator: 52 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18
14	ExprTuple	34, 40, 19
15	ExprTuple	50, 20
16	Literal
17	ExprTuple	57, 20
18	Operation	operator: 46 operands: 21
19	Operation	operator: 22 operand: 26
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Operation	operator: 52 operands: 27
25	Operation	operator: 54 operand: 32
26	Operation	operator: 29 operands: 30
27	ExprTuple	40, 31
28	ExprTuple	32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 44 operands: 35
32	Operation	operator: 52 operands: 36
33	Operation	operator: 37 operand: 42
34	Literal
35	ExprTuple	48, 39
36	ExprTuple	40, 41
37	Literal
38	ExprTuple	42
39	Operation	operator: 52 operands: 43
40	Variable
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operands: 47
43	ExprTuple	56, 50
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50, 51
48	Literal
49	Operation	operator: 52 operands: 53
50	Variable
51	Operation	operator: 54 operand: 57
52	Literal
53	ExprTuple	56, 57
54	Literal
55	ExprTuple	57
56	Literal
57	Variable

Expression of type Lambda¶

from the theory of proveit.trigonometry¶

Expression of type Lambda ¶

from the theory of proveit.trigonometry ¶