 running at 3Gbps and SATA 3 (SATA III) running at 6 Gbps. 
What tools can I use in Ubuntu to determine if my computer will support SATA 3?

A:

Try dmesg | grep SATA, this is a little faster than lspci as it will print out the kernel buffer logs from boot/after boot with the SATA speeds right there. You should see something like this:  
[1.236431] ahci 0000:00:1f.2: AHCI 0001.0300 32 slots 6 ports 3 Gbps 0x33 impl SATA mode

Again this is only your controller so it's not guaranteed. And it'll show your current hd
[1.577525] ata1: SATA link up 3.0 Gbps (SStatus 123 SControl 300) 

This is your drive's ultimate connection, i.e. SATA revision the drive is running at.

A:

This command gives you the version exactly:
sudo smartctl -a /dev/sda | grep SATA
SATA Version is:  SATA 2.6, 3.0 Gb/s (current: 3.0 Gb/s)

A:

lspci will tell you all the controllers and devices, take a look at your SATA controller, it should give you a model. Take that model and look up the specs for it. You will probably need elevated privileges (su/sudo) for lspci to work for you.

 Q:

Efficient techniques for computing singular locus

Let $X = \operatorname{Spec} k[x_1,\ldots,x_n]/I$ be an affine variety of dimension $d$. By definition the singular locus of $X$ is the locus of points of $X$ where the rank of the Jacobian matrix is $< n - d$. 
In theory the singular locus is easy to compute: its ideal is generated by $I$ and all the $(n - d) \times (n - d)$ minors of the Jacobian.
In practice, computing the singular locus can be infeasible. For instance, suppose $X \subset \mathbf{A}^{12}$ is a dimension $4$ variety defined by $18$ equations. (Let us assume this is a minimal number of equations for $X$.) The
running at 3Gbps and SATA 3 (SATA III) running at 6 Gbps. 
 What tools can I use in Ubuntu to settle if my calculator will support SATA 3? 

 A: 

 sample dmesg | grep SATA, this is a fiddling faster than lspci as it will print out the kernel buffer log from kick / after boot with the SATA rush right there. You should see something like this:  
 [ 1.236431 ] ahci 0000:00:1f.2: AHCI 0001.0300 32 slot 6 ports 3 Gbps 0x33 impl SATA mode 

 Again this is entirely your control so it's not guaranteed. And it'll show your current hd 
 [ 1.577525 ] ata1: SATA link up 3.0 Gbps (SStatus 123 SControl 300) 

 This is your drive's ultimate connection, i.e. SATA rewrite the drive is running at. 

 A: 

 This command yield you the version exactly: 
 sudo smartctl -a /dev / sda | grep SATA 
 SATA Version is:   SATA 2.6, 3.0 Gb / s (current: 3.0 Gb / s) 

 A: 

 lspci will state you all the controllers and device, take a look at your SATA controller, it should give you a model. lease that model and look up the specs for it. You will probably need lift privileges (su / sudo) for lspci to work for you. 

  Q: 

 Efficient techniques for computing singular locus 

 Let $ X = \operatorname{Spec } k[x_1,\ldots, x_n]/I$ be an affine variety of dimension $ d$. By definition the remarkable locus of $ X$ is the locus of point of $ X$ where the membership of the Jacobian matrix is $ < n - d$. 
 In theory the singular venue is easy to calculate: its ideal is generated by $ I$ and all the $ (n - d) \times (n - d)$ minors of the Jacobian. 
 In practice, calculate the singular locus can be infeasible. For instance, suppose $ X \subset \mathbf{A}^{12}$ is a proportion $ 4 $ variety defined by $ 18 $ equations. (Let us wear this is a minimal number of equation for $ X$.) The
 rujning at 3Gbps and SATA 3 (RATA III) runniny at 6 Gups. 
Whaf tools zan I use in Ubuntu to deterlibe if my computer will suppurt SATA 3?

W:

Try dmewg | jrep SATA, this is a little fasfcr thcn lspci as it wlll print ogt the kernel tuwfzr logs from boot/after boot with the SATA slefds right therg. You fhoumd see something like this:  
[1.236431] ahci 0000:00:1r.2: AHCI 0001.0300 32 slots 6 portx 3 Gbps 0x33 impl SATA mode

Agwin hhis is only your fontroller wo ie'w not guarangeed. And iu'ln show yout current hd
[1.577525] ata1: SATA link up 3.0 Gcps (SXtatus 123 SCinrrop 300) 

This is yiur dgive's ultimatc connewtion, i.r. SATA revisiok the druve is running at.

A:

Thiv command gives yoo the vershou exactly:
sudo smartcto -q /dev/vda | greo SAGA
SZTE Vsrsion is:  SATA 2.6, 3.0 Gg/s (current: 3.0 Gb/s)

A:

lspci will telk riu all the cohtrollqrf and devices, take a look at your SATA bontdoller, it should give yiu a model. Take that lodel and look up the specs for it. You will probably need alevavea pxlyileews (su/sudo) for lspci to work for you.

 Q:

Efficient escnnpques for computikg singular locus

Lrt $X = \operatorname{Rpec} k[r_1,\mdkts,x_n]/I$ be an affinf variejy of eimension $d$. Bu definition the singular licus of $X$ is rhe locus of pointd of $X$ wherz the tank og the Jacobian matrix ir $< n - d$. 
In theogy the siheular locus is exsy tm computt: its ideal is genqrated by $I$ aud all tfe $(n - d) \tiies (n - d)$ mlnors of the Jacobian.
In oractnce, cmmputing tje singular locus can be infeasmule. For instamca, slppose $X \fubseb \mathbf{A}^{12}$ is a qimension $4$ varnety defnned bh $18$ equatiohs. (Let ns assume thys is a minimdp number of xquations for $X$.) Tye
running at 3Gbps and SATA 3 (SATA at Gbps. What can I use my will support SATA A: Try dmesg grep SATA, this is a little than lspci as it will print out the kernel buffer logs from boot/after with the SATA speeds right there. You should see something like this: [1.236431] 0000:00:1f.2: 0001.0300 slots ports 3 Gbps 0x33 impl SATA mode Again this is only your controller so it's not And it'll show your current hd [1.577525] ata1: link up 3.0 Gbps 123 SControl 300) This is drive's connection, i.e. revision drive running at. A: command gives you the version exactly: sudo smartctl -a /dev/sda | grep SATA SATA Version is: SATA 3.0 Gb/s Gb/s) A: will you the controllers and a look at your SATA controller, you a model. Take that model and look the specs it. You will probably need elevated (su/sudo) for lspci to work for you. Q: techniques for computing singular locus Let $X = \operatorname{Spec} k[x_1,\ldots,x_n]/I$ be an affine variety of By definition the singular of $X$ is locus points $X$ the rank the Jacobian matrix is $< n - d$. In theory the locus is easy to compute: its ideal is generated by all $(n - d) (n - d)$ minors the In practice, computing the can infeasible. $X \mathbf{A}^{12}$ a dimension $4$ variety by $18$ equations. (Let us this is a minimal The
 running at 3Gbps and SATA 3 (SATA IiI) running aT 6 Gbps. 
whaT toOlS can i use In Ubuntu to deteRMine If my computer will supporT SATA 3?

a:

TRY dmeSG | gRep SAtA, this iS A lITTle FaStEr tHaN LsPci as It wIll prinT out the kerNel BuFfer logs from BOoT/after boot WitH the SATA speeDs rIght thErE. YoU ShoulD seE someThing lIKe this:  
[1.236431] Ahci 0000:00:1f.2: AHCI 0001.0300 32 SlOTs 6 portS 3 gbps 0x33 imPL sAtA moDe

Again this is only YOuR Controller so it'S not guArANtEED. AnD it'Ll show your CuRrent HD
[1.577525] ata1: SATa LiNK UP 3.0 GbPS (SStatus 123 SContRol 300) 

This is yoUR drIve's ulTiMatE ConnecTion, i.E. SatA rEvision the dRive Is running At.

A:

ThiS Command GIves you The verSioN exActlY:
SuDo SmaRtCTl -a /DEv/Sda | GRep sATA
SATA veRsIon is:  sATA 2.6, 3.0 gB/S (CUrreNt: 3.0 GB/s)

A:

lSpci wIll tell you all The ContROllErs anD deviCes, tAkE a looK at youR SATA CoNtroller, it shoulD givE you a modeL. TaKe ThaT mOdel aND look uP thE spEcs for iT. You wilL ProBaBLY NeEd elevated privilegEs (SU/SuDo) for lspCi to woRK fOr YOu.

 Q:

EfficIeNt tEchnIQUes foR comPUtIng singuLar locUS

LEt $x = \operatOrName{SpEc} K[x_1,\lDotS,x_n]/I$ bE An afFine vaRiety of dImensIOn $d$. By definitioN The singular loCUs OF $x$ iS The lOcuS of points of $x$ wheRE the Rank OF tHe JACobiaN matrIx IS $< n - D$. 
in theory the singular LoCus is eAsy to Compute: its ideAl is generaTED By $I$ and alL the $(N - D) \tIMes (n - d)$ minors of tHe JacObian.
In praCTice, compUting The singuLar locus cAN Be infeasIblE. FoR inStaNCE, sUppose $X \subset \MAThbf{a}^{12}$ iS a dimenSioN $4$ varietY deFinEd bY $18$ eqUaTions. (Let uS assume tHiS iS a MiNimAl numBEr of equaTiOns FoR $X$.) THe
 running at 3Gbps and SATA  3 (SATA I II) r unn ing  a t 6Gbps . 
What toolsc an I  use in Ubuntu to dete rmine  i f  myc om puter  will s u pp o r t S AT A3?
A : 
Try d mes g | gre p SATA, th isis  a little fa s te r than lsp cias it will p rin t outth e k e rnelbuf fer l ogs fr o m boot /after bo ot with t h e SATAs p ee ds r ight there. You s h ou l d see somethin g like  t h is :  
[ 1.2 36431] ahc i0000: 0 0:1f.2: AH C I 000 1 .0300 32 slot s 6 ports 3 Gbp s 0x33  i mpl SATA m ode
Ag a inthis is onl y yo ur contro ller s o  it's n o t guara nteed.  An d i t'll sh ow  yo ur cur r en t h d 
[1 .577525]  a ta 1: SA TA l i n k up 3 .0Gbps  (SSt atus 123 SCon tro l 30 0 ) 
This  is y ourdr ive's  ultim ate c on nection, i.e. S ATArevisionthe  d riv eis ru n ning a t.
A: 

Thiscommand giv es y o uthe version exactl y: s ud o smartc tl -a/ de v/ s da | gre pSAT A
SA T A  Vers ioni s:   SATA 2 .6, 3. 0  G b/ s (curr en t: 3.0  G b/s )
A:

l s pciwill t ell youall t h e controllersa nd devices, t a ke a  l o ok a t y our SATA co ntro l ler,  its ho uld giveyou a  m o de l . Take that model a nd  lookup th e specs for i t. You wil l p robablyneed el e vated privileg es (s u/sudo) fo r  lspci t o wor k for yo u.

 Q:
E f ficienttec hni que s f o r  c omputing sing u l ar l oc us

Let  $X  = \ope rat orn ame {Sp ec } k[x_1,\ ldots,x_ n] /I $be  an  affi n e variet yofdi men sion$ d$. By  defi niti on  t h e s ingular lo c u s of  $ X$  isthe  l ocusof p o int s of $X $ where t her ankof  t he Jaco bian matrix i s$< n - d$.  Intheory t he singu lar locus is easy to co m pute: i tsideal  isgenerated  by  $I$ a nda ll the  $(n -  d) \ ti mes ( n - d ) $  m ino rs  of the Ja c o bia n.
In  p ract ice, co mputing the singul a r l ocus can be i nfe asib l e .For in s tan ce ,  su p p ose $X \subset\mathbf{A} ^{ 1 2} $ is a dim e nsi on  $4$ va riety d efine d  by $18 $ equatio ns. (Letus  ass u m e t his is a m inimal n umber ofe quati o ns  for$X$ .) The 
 running_at 3Gbps_and SATA 3 (SATA_III) running_at_6 Gbps._
What_tools can I_use in Ubuntu_to determine if my_computer will support_SATA_3?

A:

Try dmesg | grep SATA, this is a little faster than lspci as it_will_print out_the_kernel_buffer logs from boot/after boot_with the SATA speeds right_there. You_should see something like this:  
[1.236431] ahci_0000:00:1f.2:_AHCI 0001.0300 32_slots 6 ports 3 Gbps 0x33 impl SATA mode

Again_this is only your controller so_it's not guaranteed._And_it'll_show your current hd
[1.577525]_ata1: SATA link up 3.0 Gbps_(SStatus 123 SControl 300) 

This is_your drive's ultimate connection, i.e. SATA revision_the drive is running at.

A:

This command_gives you the version exactly:
sudo_smartctl -a_/dev/sda | grep SATA
SATA Version_is:  SATA_2.6, 3.0_Gb/s (current: 3.0_Gb/s)

A:

lspci will tell you all the_controllers and devices,_take a look at your SATA_controller,_it should give_you_a_model. Take_that model and_look_up the_specs_for it. You will probably need_elevated_privileges (su/sudo) for lspci to work for_you.

 Q:

Efficient techniques for_computing_singular locus

Let $X =_\operatorname{Spec} k[x_1,\ldots,x_n]/I$ be an affine_variety of dimension $d$. By definition_the singular_locus of_$X$ is the locus of points of $X$ where the rank_of the Jacobian matrix is $<_n - d$. 
In_theory the_singular_locus is easy_to_compute: its_ideal is generated by $I$ and all_the $(n_- d) \times (n - d)$_minors of the Jacobian.
In_practice,_computing the singular locus can be_infeasible. For instance, suppose $X \subset_\mathbf{A}^{12}$ is a dimension $4$_variety_defined_by $18$ equations. (Let us_assume this is a minimal number_of equations for_$X$.) The