Expression of type ExprTuple

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 ExprTuple, a, b, c, r
from proveit.numbers import Abs, Exp, Mult, e, frac, i, subtract, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = ExprTuple(Abs(subtract(Mult(r, Exp(e, Mult(i, a)), c), Mult(r, c, Exp(e, Mult(i, b))))), Mult(two, r, c, Sin(frac(Abs(subtract(a, b)), two))))

expr:

# 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(\left|\left(r \cdot \mathsf{e}^{\mathsf{i} \cdot a} \cdot c\right) - \left(r \cdot c \cdot \mathsf{e}^{\mathsf{i} \cdot b}\right)\right|, 2 \cdot r \cdot c \cdot \sin{\frac{\left|a - b\right|}{2}}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 23 operand: 5
2	Operation	operator: 39 operands: 4
3	ExprTuple	5
4	ExprTuple	20, 26, 27, 6
5	Operation	operator: 33 operands: 7
6	Operation	operator: 8 operand: 12
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	Operation	operator: 39 operands: 13
11	Operation	operator: 41 operand: 18
12	Operation	operator: 15 operands: 16
13	ExprTuple	26, 17, 27
14	ExprTuple	18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 31 operands: 21
18	Operation	operator: 39 operands: 22
19	Operation	operator: 23 operand: 29
20	Literal
21	ExprTuple	35, 25
22	ExprTuple	26, 27, 28
23	Literal
24	ExprTuple	29
25	Operation	operator: 39 operands: 30
26	Variable
27	Variable
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprTuple	43, 37
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	Operation	operator: 39 operands: 40
37	Variable
38	Operation	operator: 41 operand: 44
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	44
43	Literal
44	Variable