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 ModAbs, Mult, frac, one, subtract
from proveit.physics.quantum.QPE import _phase, _two_pow_t

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

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(\frac{2^{t} \cdot \left|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1}}{2^{t}}, \frac{\left|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1}}{1}\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: 17 operands: 3
2	Operation	operator: 17 operands: 4
3	ExprTuple	5, 22
4	ExprTuple	8, 12
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	22, 8
8	Operation	operator: 9 operands: 10
9	Literal
10	ExprTuple	11, 12
11	Operation	operator: 13 operands: 14
12	Literal
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operand: 23
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Variable
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Literal