Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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, m
from proveit.numbers import Floor, ModAbs, Mult, Neg, subtract
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Mult(_two_pow_t, _phase)
expr = ExprTuple(ModAbs(subtract(m, sub_expr1), _two_pow_t), Neg(ModAbs(subtract(m, Floor(sub_expr1)), _two_pow_t)))

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|m - \left(2^{t} \cdot \varphi\right)\right|_{\textup{mod}\thinspace 2^{t}}, -\left|m - \left\lfloor 2^{t} \cdot \varphi\right\rfloor\right|_{\textup{mod}\thinspace 2^{t}}\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: 8 operands: 3
2	Operation	operator: 16 operand: 6
3	ExprTuple	5, 24
4	ExprTuple	6
5	Operation	operator: 12 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	14, 10
8	Literal
9	ExprTuple	11, 24
10	Operation	operator: 16 operand: 21
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Variable
15	Operation	operator: 16 operand: 18
16	Literal
17	ExprTuple	18
18	Operation	operator: 19 operand: 21
19	Literal
20	ExprTuple	21
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Literal