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, r, theta
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(r, Mult(r, Exp(e, Mult(i, theta))))), Mult(two, r, Sin(frac(Abs(theta), 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|r - \left(r \cdot \mathsf{e}^{\mathsf{i} \cdot \theta}\right)\right|, 2 \cdot r \cdot \sin{\frac{\left|\theta\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: 21 operand: 5
2	Operation	operator: 29 operands: 4
3	ExprTuple	5
4	ExprTuple	19, 23, 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operand: 12
7	Literal
8	ExprTuple	23, 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 29 operands: 20
18	Operation	operator: 21 operand: 32
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	32
23	Variable
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Variable