# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = Equals(subtract(_two_pow__t_minus_one, two), subtract(Mult(frac(one, Exp(two, one)), _two_pow_t), two))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(2^{t - 1} - 2\right) = \left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 17
operands: 5
4Operationoperator: 17
operands: 6
5ExprTuple7, 9
6ExprTuple8, 9
7Operationoperator: 27
operands: 10
8Operationoperator: 11
operands: 12
9Operationoperator: 25
operand: 29
10ExprTuple29, 14
11Literal
12ExprTuple15, 16
13ExprTuple29
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Operationoperator: 27
operands: 21
17Literal
18ExprTuple24, 22
19Literal
20ExprTuple30, 23
21ExprTuple29, 24
22Operationoperator: 25
operand: 30
23Operationoperator: 27
operands: 28
24Literal
25Literal
26ExprTuple30
27Literal
28ExprTuple29, 30
29Literal
30Literal