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, k, t
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(frac(one, Exp(two, frac(t, two))), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, 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{1}{2^{\frac{t}{2}}}, \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\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: 14 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	48, 6
4	Literal
5	ExprTuple	7
6	Operation	operator: 42 operands: 8
7	Lambda	parameter: 39 body: 10
8	ExprTuple	46, 11
9	ExprTuple	39
10	Conditional	value: 12 condition: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	47, 46
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	39, 22
20	Operation	operator: 42 operands: 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	39, 47
26	Literal
27	ExprTuple	30, 31
28	Literal
29	Operation	operator: 32 operands: 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	46, 36, 37, 38, 39
34	Literal
35	ExprTuple	40, 41
36	Literal
37	Literal
38	Literal
39	Variable
40	Operation	operator: 42 operands: 43
41	Operation	operator: 44 operand: 48
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48
46	Literal
47	Variable
48	Literal